Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values of the remaining five trigonometric functions of theta

Answers

Answer 1

The exact values of the remaining five trigonometric functions of theta are

sinθ = √3/2cosecθ = 2/√3cosθ = -1/2secθ = -2 cotθ = -1/√3

Since tanθ = -√3.

The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.

The next trigonometric function of θ is cotθ.

cotθ = 1/tanθ

= 1/-√3

= -1/√3.

Also, tan²θ + 1 = sec²θ

Substituting tanθ = -√3 into the equation, we have

(-√3)² + 1 = sec²θ

3 + 1 = sec²θ

sec²θ = 4

secθ = ±√4

secθ = ±2

Since θ is in the quadrant II,

secθ = -2

Also, cosθ = 1/secθ

= 1/-2

= -1/2

Also, cot²θ + 1 = cosec²θ

Substituting cotθ = -1/√3 into the equation, we have

(-1/√3)² + 1 = cosec²θ

1/3 + 1 = cosec²θ

cosec²θ = 4/3

cosecθ = ±√(4/3)

cosecθ = ±2/√3

Since θ is in the quadrant II,

cosecθ = +2/√3

Also, sinθ = 1/cosecθ

= 1/2/√3

= √3/2

So, the exact values of the remaining five trigonometric functions of theta are

sinθ = √3/2cosecθ = 2/√3 cosθ = -1/2secθ = -2cotθ = -1/√3.

Learn more about trigonometric functions here:

https://brainly.com/question/4515552


Related Questions

which expression has the same value as tan (-45degrees)?

Answers

Answer: B

Step-by-step explanation:

Trust

A book club charges an initial joining fee of $30.00. The cost per book is $7.00. The graph shows the cost of belonging to the club as a function of books purchased. How will the graph change if the cost per book goes up by $1.50? (The new function is shown by the dotted line.)

Answers

Answer:

$82.50

Step-by-step explanation:

You add seven dollars to $1.50 and you would get the sum of 8.50 then you multiply the amount of books purchased. The Equation is 5($8.50) + $30.00= 82.50

Sorry if I get this wrong.

This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 7%.



Calculate the amount of sales tax Cassie will pay on the purchase. Round to the nearest cent if necessary.



sales tax: $

Listen to the complete question
Part B
Fill in the blank question.
How much will Cassie pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.



total cost: $

Answers

Answer:

$10.12

Step-by-step explanation:

Step one:

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87


What is the equation for the parabola with a focus F(13/11,0)?

Answers

Answer:

B.ON THE EDGE

Step-by-step explanation:

what is the equation for: 32 is the sum of a number x and 9

Answers

Answer:

x + 9 = 32

Step-by-step explanation:

answer for x is 32 - 9 = 23

Please help derivitive
Please dont comment if you dont know …

Answers

[tex]\lim \limits_{x \to 0^{+}} \left( \csc x + \dfrac 1x \right)\\=\lim \limits_{x \to 0^{+}} \csc x + \lim \limits_{x \to 0^{+}} \dfrac 1x\\\\=\infty[/tex]

the title block in a working drawing indicates that the scale is a ratio of 1 and 5. This means that the real measurement of the machine is five times the what?

Answers

A scale of 1:5 indicates that real measurement of the machine is five times one unit in the drawing.

The title block on a working drawing shows some important details that may be relevant in reading the drawing. One of such important details is the scale of the drawing.

The scale tells us how the size of the drawing relates to the actual size in the real world. Hence, a scale of 1:5 indicates that real measurement of the machine is five times one unit in the drawing.

Learn more about scale drawing: https://brainly.com/question/147532

pls help me
I m giving brainliest

Answers

Step-by-step explanation:

the general line equation format is

y = ax + b

a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".

b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.

(i)

A (3, 5)

B (5, 9)

x changes by +2 (from 3 to 5).

y changes by +4 (from 5 to 9).

so, the slope (or gradient) is +4/+2 = 2

(ii)

the semi-finished equation is

y = 2x + b

let's use A to get b :

5 = 2×3 + b = 6 + b

b = -1

and the full equation is

y = 2x - 1

(iii)

for point (4, k) we get

k = 2×4 - 1 = 8 - 1 = 7

three less than a number is -18

Answers

Answer:

-15

Step-by-step explanation:

work in reverse

-18 is three less than something

that means that something is 3 more than -18

so

add 3 to -18

-18+3= -15

If angle 1 is 110°, what would the other angle measures have to be in order for m || n andq || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °

Answers

Answer:

8

Step-by-step explanation:

Answer:

ANGLE2=110° ANGLE3=70° ANGLE4=70°

20 charecters lol pls solve

Answers

Answer:

-3x+12

Since we are adding like terms you add everything that has an "x" after it [(3.4x) + (-5.4x) + (-x)] it all that adds up to -3x and the you add the 12 to it. It could also be written 12-3x

(15 points) Critique Reasoning Jamie says that the
expressions 6x - 2x + 4 and 4(x + 1) are not
equivalent because one expression has a term
that is subtracted and the other does not. Do
you agree? Explain.
a

Answers

Answer:

they are the same

Step-by-step explanation:

6x - 2x + 4 ← collect like terms

= 4x + 4

and

4(x + 1) ← distribute parenthesis by 4

= 4x + 4

The 2 expressions are equivalent to 4x + 4

Answer:

No, Jamie is incorrect

Step-by-step explanation:

No, because in the expression 4(x+1)  you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.

Also in the expression 6x-2x+4  ,you will first need to subtract 2x from  6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4

Our final answer is:

6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4

Elements that do not belong to a set belong to its

Answers

Answer:

What do you mean for this question?

Step-by-step explanation:

Give specific details

what is the value of x

Answers

Answer:

x = 32

Step-by-step explanation:

this is an equilateral triangle where all sides measure the same value; therefore, 2x-4 = 5y

since we are solving for 'x' we can set up this equation:

3(2x-4) = 180

6x - 12 = 180

6x = 192

x = 32

This morning, Raina's car had 23.21 gallons of fuel. Now, 1.5 gallons are left. How much fuel did Raina use?​

Answers

Total Gallons = Number of Gallons used + Number of Gallons she has left

Let x represent number of gallons of fuel used

23.21 gallons = x gallons + 1.5 gallons
x = 21.6 gallons were used

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )

Answers

Answer:

x=7.85

Step-by-step explanation:

Give the triangles we know that:

[tex] \frac{cd}{fh} = \frac{de}{hg} = \frac{ce}{gf} [/tex]

Now we can substitute like usual

[tex] \frac{78}{fh} = \frac{117}{54} = \frac{ce}{5x + 1} [/tex]

Now we simplify the fraction in the middle

the middles fraction will =13/6

Therefore:

[tex] \frac{78}{fh} = \frac{13}{6} [/tex]

so 13fh=468

Therefore: fh=36

Now we can use the Pythagorean theorem

so

[tex]gf = \sqrt{ {54}^{2} - {36}^{2} } [/tex]

so gf=18√5

so 5x+1=18√5

so 5x=-1+18√5

so x=7.85

(I'm not too sure about this one tho)

The vertice of triangle ABC are A(8,4), B(6,3) and C(5-5). Find the angle between the side AB and BC.​

Answers

Answer:

Step-by-step explanation:

Use law of cosines

c² = a² + b² - 2abcosθ

cosθ = (c² - a² - b²) / -2ab

c = length of AC = √(8 - 5)² + (4 - (-5))² = √90

b = length of AB = √(8 - 6)² + (4 - 3)² = √5

a = length of BC = √(6 - 5)² + (3 - (-5))² = √65

cosθ = (√90² - √65² - √5²) / -2√65√5

cosθ = 20 / -36.05551...

cosθ = - 0.5547001

θ = 123.69°

Genes are sections of DNA that code for a particular trait. Genes are?

Answers

Answer:

Genes are DNA transferred to off spring by parents

Answer:

Genes are sections of DNA that code for a particular trait. Genes are nucleic acids.

Step-by-step explanation:

find the following right triangle, find the side length x

Answers

Answer:

x=41

Step-by-step explanation:

9²+40²=x²

81+1600=x²

1681=x²

√1681=√x²

41=x

help me please i'll mark as brainliest asap​

Answers

Answer:

a. A(x) = 3x² - 8x + 5

b. x = ⁸/₃

Step-by-step explanation:

a.

A(x) = shaded area

A(x) = (2x - 3)² - (x - 2)²

= 4x² - 12x + 9 - (x² - 4x + 4)

= 4x² - x² - 12x + 4x + 9 - 4

= 3x² - 8x + 5

b.

ΔABF area = ⁵/₄ cm²

A(x) = 4(⁵/₄)

= 5

Substitution:

3x² - 8x + 5 = A(x) = 5

3x² - 8x + 5 = 5

3x² - 8x = 0

x(3x - 8) = 0

3x - 8 = 0

x = ⁸/₃

x = 0

Since x > 2, x = 0 is not valid;

So, x = ⁸/₃

Which of the following statements best describes the location of −(−1) on a number line? (5 points)

Question 6 options:

1)

It is 1 unit to the left of 0.


2)

It is 1 unit to the right of 0.


3)

It is 1 unit to the right of 1.


4)

It is 1 unit to the left of 1.

Answers

Answer:

It is 1 unit to the right of 0.

Step-by-step explanation:

The figure shown is to be painted on a road sign. Which of the following best describes the two polygons that form the figure?

A. A rectangle and an isosceles trapezoid
B. A rectangle and a rhombus
C. A rectangle and a parallelogram
D. A rectangle and an isosceles triangle​

Answers

Answer:

D: A rectangle and an isosceles triangle​

Step-by-step explanation:

A recangle for the base of the arrow, and an isosceles triangle​ to form the full arrow.

The answer will be option D which is a rectangle and an isosceles triangle.

What is an isosceles triangle?

The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.

As we can see in the figure there are one isosceles triangle and a rectangle are joined together to form an arrow.

Thus the answer will be option D which is a rectangle and an isosceles triangle.

To know more about the isosceles triangle follow

https://brainly.com/question/1475130

#SPJ2

f(x)=x^2-7 and h(x)=7x-5, then f(h(2))= ?

Answers

Answer:    74

==================================================

Work Shown:

h(x) = 7x-5

h(2) = 7(2)-5

h(2) = 14-5

h(2) = 9

f(h(2)) = f(9)

f(x) = x^2-7

f(9) = 9^2-7

f(9) = 81-7

f(9) = 74

f(h(2)) = 74

-----------

Here's a slightly alternative approach:

f(x) = x^2 - 7

f(h(x)) = ( h(x) )^2 - 7

f(h(x)) = ( 7x-5 )^2 - 7

f(h(2)) = ( 7*2-5 )^2 - 7

f(h(2)) = ( 14-5 )^2 - 7

f(h(2)) = ( 9 )^2 - 7

f(h(2)) = 81 - 7

f(h(2)) = 74

Solve for X


show your work

Answers

Answer:

alternate exterior angles are equal .

17x + 2 = 18x - 2

x = 2 + 2

x = 4

Step-by-step explanation:

I believe it’s x = 4

5. 4
Which input value produces the same output value for
the two functions on the graph?
(
*)
3
NO
O x= -1
O x = 0
O x= 1
O x= 2
-5 -3 -2 -
4
х
91x)

Answers

Answer:

x=1......................

Tara placed $1200 in a savings account which compounds interest continuously at a rate of 1.4%.


How much will she have in the account after 3 years?

Round your answer to the nearest dollar.

Do NOT round until you have calculated the final answer.

Answers

Answer:

$1,251

Step-by-step explanation:

Formula: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Plug the values into the formula; solve:

[tex]r = \frac{r}{100}[/tex]

[tex]r = \frac{1.4}{100}[/tex]

[tex]r = 0.014[/tex]

0.014 rate per year

[tex]A = Pe^{rt}[/tex]

[tex]A = 1,200.00^{(2.71828)}^{(0.014)(3)}[/tex]

[tex]A = $1,251.47\\[/tex]

1,251.47 is 1251 rounded because the first value after the decimal point is not greater or equal to 5.

Answer:

1251

Step-by-step explanation:

For what value(s) of k is + 3 a factor of 3 + 5 2 + − 9
FAST FASTTTT

Answers

Answer:

56

Step-by-step explanation:

56 would be ya answer

What is 5x + 12 < 2 ?

Answers

Answer:

x < -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

5x + 12 < 2

Step 2: Solve for x

[Subtraction Property of Equality] Subtract 12 on both sides:                       5x < -10[Division Property of Equality] Divide 5 on both sides:                                 x < -2

Answer:

x < - 2

Step-by-step explanation:

5x + 12 < 2 ( subtract 12 from both sides )

5x < - 10 ( divide both sides by 5 )

x < - 2

Which choice is equivalent to the product below?
V8,5
O A. 4/10
O B. 10-12
C. 13
O D. 22/10

Answers

Answer:

Option D

2√10

Step-by-step explanation:

√8 • √5 = √8 × 5 = √40 = 210

Thus, √8 • √5 = 2√10

-TheUnknownScientist 72

There are 8 triangles and 6 circles. What is the simplest ratio of total circles to total shapes

Answers

Ratio of total circles to total shapes is 4 : 7

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 8 triangles and 6 circles. The ratio of total circles to total shapes is given by:

Ratio of total circles to total shapes = 8 circles : (8 + 6) shapes

Ratio of total circles to total shapes = 8 : 14 = 4 : 7

Find out more about equation at: https://brainly.com/question/2972832

Other Questions
Is it possible for a primary consumer to be an omnivore or carnivore? PLEASE HELP ASAP TENTH GRADE GEOMETRY Choose the angle which is represented by the name.R been trying to solve this, need help Can someone plz help me? :( How are gods covenants with the Jewish people related to the Jewish teachings about ethics and justice Help a sis out ??Write a function rule for the area of a triangle whose height is 4 in, more than twice the lengthof its base. What is the area of the triangle when the length of its base is 16 in.?A. A = 262 + bC. A = 262 + bA = 144 in?A = 528 in.B. A = b2 + 2bA = 288 inD. A = 262 + 4bA = 576 inODB.CSES Which two quotations include information that should be included in a summary of thetext?"Because she was the oldest of 11 children, her job was to herd the animals fromsunrise to sunset on 18,000-foot mountains." (paragraph 1)O "Clouds blanketed the blue sky in minutes and pelted Dorje with hail." (paragraph 2)"At first, she couldn't see the beast because its gray, furry body had dark brown dotsand lines that blended with the landscape" (paragraph 3)"Her parents were busy planting and harvesting the barley, buckwheat, and potatoesthat made up the bulk of their diet." (paragraph 7)e"When she is not painting or making jewelry, Dorje gives talks at schools and aroundthe world to bring awareness to her culture and the Dolpo region." (paragraph 11) The charge on an ion isa.always positive.b.always negative.C.either positive or negative. If the speed of the magnet is doubled, the induced voltage is ________ . twice as great four times as great half as great unchanged The free speech movement: _____________a. began in Port Huron to protest a campus ban on political literature. b. had little support among college-age students at the time.c. failed in its efforts to establish free speech on college campuses. d. began in Berkeley to protest a campus ban on political groups convening and distributing literature at a central meeting place. e. began in Los Angeles to protest a campus ban on political literature. Help me to answer this David is deciding between two parking garages. Garage A charges an initial fee of $7 to park plus $3 per hour. Garage B charges an initial fee of $4 to park plus $4 per hour. Let A represent the amount Garage A would charge if David parks for t hours, and let B represent the amount Garage B would charge if David parks for hours . Write an equation for each situation , in terms of t, and determine which garage would be cheaper if David needs to park for 2 hours . -Which image shows in nonrenewable resource? Consider the problem: A set of books that are each 1.5 inches wide are being organized on a bookshelf that is 36 inches wide. How many books can fit on the shelf?a. Complete the multiplication equation and the division equation to represent the situation. Use a ? to represent the unknown in the equation. Write your answer as a decimal to the nearest tenth if necessary.multiplication equation: ? () = division equation: = ?b. How many books can fit on the shelf? Use a diagram, if needed. books a point f(3, 1) is translated along the vector 5, 1.what are the coordinates of the image f ? Someone help me pls Mis amigos (ver) el partido de baloncesto present tense help me it's algebra and dont tell me to look at the lesson :) a spring with a spring constant of 65 n/m is displaced -94cm. what is the magnitude of the force exerted by the spring