PLEASE HELP!!!!
Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
sin(θ) =
cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =
Answers
cos(theta)=8/17
tan(theta)=-15/8
csc(theta)=-17/15
sec(theta)=17/8
cot(theta)=-8/15
Hope this helps
Answers:
sin(θ) = -15/17 cos(θ) = 8/17 tan(θ) = -15/8 csc(θ) = -17/15 sec(θ) = 17/8 cot(θ) = -8/15=======================================================
Explanation:
Refer to the diagram below. The point (8,-15) is in quadrant 4, which is the southeast quadrant. A right triangle forms where the hypotenuse goes from the origin to the terminal point in question. After applying the pythagorean theorem, the hypotenuse is 17 units long.
Opposite the reference angle θ, greek letter theta, the side is -15. Usually negative lengths are not allowed and don't make any sense; however, I'm making this negative to ensure that sin(θ) ends up negative. This will help with other trig ratios as well.
So,
sin(angle) = opposite/hypotenuse
sin(θ) = -15/17
-----------------
The cosine ratio will involve the adjacent and hypotenuse
cos(angle) = adjacent/hypotenuse
cos(θ) = 8/17
------------------
Tangent is opposite over adjacent
tan(angle) = opposite/adjacent
tan(θ) = -15/8
------------------
The functions csc(θ), sec(θ), and cot(θ) are the functions cosecant, secant, and cotangent in that order.
They represent the reciprocal of sine, cosine, and tangent in that order as well.
Eg: sec(θ) is the reciprocal of cos(θ)
This means,
csc(θ) = -17/15 which is the flip of sin(θ) = -15/17sec(θ) = 17/8 which is the flip of cos(θ) = 8/17cot(θ) = -8/15 which is the flip of tan(θ) = -15/8As an alternative, you could also say
csc(θ) = hypotenuse/opposite = 17/(-15) = -17/15sec(θ) = hypotenuse/adjacent = 17/8cot(θ) = adjacent/opposite = -15/8------------------------
Here's a list of formulas that you can write down on a reference sheet
sin(θ) = y/h cos(θ) = x/h tan(θ) = y/x csc(θ) = h/y sec(θ) = h/x cot(θ) = x/ywhere h is the hypotenuse and h = sqrt(x^2+y^2). Notice that something like tan = y/x is the reciprocal of cot = x/y. The x and y refers to the coordinates of the terminal point given to you. Make sure to reduce all fractions as much as possible. In our case, none of the fractions can be reduced any further.
Related Questions
solve the inequality 3/5x +30>150
Answers
Answer:
Step-by-step explanation:
3/5x+30=150
We move all terms to the left:
3/5x+30-(150)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We add all the numbers together, and all the variables
3/5x-120=0
We multiply all the terms by the denominator
-120*5x+3=0
Wy multiply elements
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We move all terms containing x to the left, all other terms to the right
-600x=-3
x=-3/-600
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Solve the system of equations.
{y=30x+10y=5x2−25
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What percent of 80 is 20? Answer pla
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Answer:
25%
Step-by-step explanation:
[tex] \frac{20}{80} = \frac{1}{4} = 0.25 = 25\%[/tex]
Kyle is buying a $220 bicycle if the bicycle is on sale for 35% off how much will he save
Answers
Answer:
$77
Step-by-step explanation:
Okay so first, we know that the bicycle is 220 dollars. So we got to multiply that to the percent. We can't muiltiply it into the percent yet so we turn that percent into 0.35
220 * 0.35
This equals to 77. That's the answer but it's not that simple, cause we aren't finished!
So we know that 35 percent of 220 is 77 dollars. So subtract that to 220!
220 - 77
This is equal to 143. Now how much will he save? He will save 220 - 143, which is 77! That's how we know the answer! I'm sure this is correct, if itsn't please comment! Have a great day!
Answer:
$143
Step-by-step explanation you wanna see how much 35% is out of 220
35% = 0.35
220 * 0.35 = 77 = discount
Now you want to see how much it will be when the discount is applied
220-77 = 143
The bicycle is $143 when discount is applied, you save $77
Complete the function table for each equation
Answers
Answer:
y=-32, 0, -16, -4, 16
Step-by-step explanation:
y=4(-6)-8= -32
y=4(2)-8 = 0
y=4(-2)-8 = -16
y=4(1) -8 = -4
y=4(6) -8= 16
For the given equation of the line, the complete table is attached below.
Use the concept of the equation of line defined as:
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
The given equation of a line is,
y = 4x - x
To complete the table:
Put x = -6 in this equation,
y = (-4)(-6) - 8
y = 16
Put x = 2 in the equation,
y = (-4)(2) - 8
y = -16
Put x = -2 in the equation,
y = (-4)(-2) - 8
y = 0
Put x = 1 in the equation,
y = (-4)(1) - 8
y = -12
Put x = 6 in the equation,
y = (-4)(6) - 8
y = -32
The complete table is attached below.
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Which of the following is the correct point-slope equation for the line that
passes through the point (-3,-9) and is parallel to the line given by
y = 2.5x - 20?
O A. Y-3 = 2.5(x-9)
B. y + 3 = 2.5(x + 9)
O C. y + 9 = 2.5(x + 3)
O D. Y- 9 = 2.5(x-3)
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Which words best fill in the blank indicate a shift in setting?
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Answer:
4.upon
Step-by-step explanation:
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Answer:
X is 15 and Y is 40° That's the answer
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Step-by-step explanation:
Answer:
[tex]5^{-1}[/tex]
Step-by-step explanation:
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Since they have the same base we can combine the exponents. Since we have a division sign, we add the exponents
5⁻⁴⁻³
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Please help me with this problem
ln -3x + ln 4 = ln 58
Answers
9514 1404 393
Answer:
x = -29/6 = -4 5/6
Step-by-step explanation:
The equation simplifies to ...
ln(-3x·4) = ln(58)
Taking antilogs, the equation becomes ...
(-3x)(4) = 58
Dividing by -12 shows us the value of x.
x = -58/12
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__
The applicable rule of logarithms is ...
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x = 7
I need help like right now. Im brain dead
Answers
Answer:
y-intercept: [tex](0,-\frac{5}{2} )[/tex]
x-intercept: [tex](-2,0)[/tex]
Step-by-step explanation:
Hi there!
Important things to note:
the y-intercept occurs when x=0the x-intercept occurs when y=01) Find the y-intercept
[tex]-5x-4y=10[/tex]
Substitute x with 0
[tex]-5(0)-4y=10\\0-4y=10\\-4y=10[/tex]
Divide both sides by -4
[tex]\frac{-4y}{-4} =\frac{10}{-4} \\y=-\frac{5}{2}[/tex]
Therefore, the y-intercept is [tex]-\frac{5}{2}[/tex]. When written in (x,y) form, x will always be 0 while y is the y-intercept:
[tex](0,-\frac{5}{2} )[/tex]
2) Find the x-intercept
[tex]-5x-4y=10[/tex]
Substitute y with 0
[tex]-5x-4(0)=10\\-5x-0=10\\-5x=10[/tex]
Divide both sides by -5
[tex]-5x=10\\\frac{-5x}{-5}= \frac{10}{-5} \\x=-2[/tex]
Therefore, the x-intercept is -2. When written in (x,y) form, x will always be the x-intercept while y is always 0:
[tex](-2,0)[/tex]
I hope this helps!
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Answers
Answer:
C.
Step-by-step explanation:
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If this helps please mark as brainliest
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Step-by-step explanation:
I have proof links, and I took the test
In 2017 the population of Rexburg, Idaho was 28,337 people. The population was expected to grow at a rate of about 1.26% per year. Based on these numbers, what would we predict the population of Rexburg will be in the year 2022?
(Round to the nearest whole number.)
Answers
Answer:
30,122
Step-by-step explanation:
This probably isn't the fastest way to solve but....
28,337x1.26%= 357
357x5=1785
28,337+1785=30,122
The 5 came from the # of years the population is increasing
We are required to find the population of Rexburg will be in the year 2022
The population of Rexburg will be in the year 2022 is 30,122 people
Given:
2017 population = 28,337 people
Growth rate per year = 1.26%
let
n = number of years between current and predicted
= 2022 - 2017
n = 5 years
Yearly growth rate = 28,337 × 1.26%
= 28,337 × 0.0126
= 357.0462
Predicted population in 2022 = 2017 population + (357.0462 ×5)
= 28,337 + 1,785.231
= 30,122.231
Approximately, 30,122 people in 2022.
Therefore, the population of Rexburg will be in the year 2022 is 30,122 people
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Step-by-step explanation:
A cone has a base radius of 3 cm and a slant height of 5 cm.
Find h, the perpendicular height of the cone.
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Answer:
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Step-by-step explanation:
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Answer:
I=4 (Slant height)
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Step-by-step explanation:
Imagine inclination, peprendicular height and radius as a triangle, so this will have a 90 degrees angle and Pythagor theorem will imply to the calculations, as :
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9514 1404 393
Answer:
100°
Step-by-step explanation:
Arc BC is twice the measure of inscribed angle BEC, so is ...
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Step-by-step explanation:
The inscibed angle E is 1/2 the measure of the central angle P so P is 100 degrees, and arc BC is also 100 degrees.
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
2.565
Step-by-step explanation:
Hope that this helps!
Which fraction correctly represents 0.63?
A 5/12
B 7/11
C 2/3
D 9/13
Answers
Answer:
7/11
Step-by-step explanation:
take the numirater and divide by denominator
7÷11=0.6363....
Answer:
like owlowlowl said '7/11'
Write the point -slope form of the equation of the line (-2,5), slope =6
Answers
Answer:
y - 5 = 6(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 6 and (a, b) = (- 2, 5) , then
y - 5 = 6(x - (- 2)) , that is
y - 5 = 6(x + 2)
[tex]2 \times (2 - 6 + 3 + 64 \times 3)[/tex]
Who will get the answer first?
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Answer:
382
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
2 × (2 - 6 + 3 + 64 × 3)
Step 2: Evaluate
(Parenthesis) Multiply: 2 × (2 - 6 + 3 + 192)(Parenthesis) Subtract: 2 × (-4 + 3 + 192)(Parenthesis) Add: 2 × (-1 + 192)(Parenthesis) Add: 2 × 191Multiply: 382i need help pls!
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Alternate interior
This is your answer
Answer:
alternative .....................
From the equation, find the axis of symmetry of the parabola. y = 3 x squared minus 12 x + 11 a. x = negative 2 c. x = 1 b. x = 2 d. x = negative 1 Please select the best answer from the choices provided A B C D
Answers
Answer:
the axis of symmetry would be: b. x=2
The equation of the axis of symmetry of the parabola will be x = 2. Then the correct option is B.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = 3x² - 12x + 11
Convert the equation into a vertex form. Then we have
y = 3x² - 12x + 11
y = 3x² - 12x + 12 - 1
y = 3(x² - 4x + 4) - 1
y = 3(x - 2)² - 1
The equation of the axis of symmetry of the parabola is given as,
x - 2 = 0
x = 2
The equation of the axis of symmetry of the parabola will be x = 2. Then the correct option is B.
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To build a computer, Tom needs to buy a motherboard for £ 120, and a CPU for
£ 100.Then find the total cost of building 10 computer ?
Answers
Answer:
£2200
Step-by-step explanation:
1 computer = £120 + £100
1 computer = £220
10 computers = £220 x 10
10 computers = £2200