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Which of the following are trigonometric identities? Select all that apply. (3)
What is a simplified form of the expression sec^2 x-1/sinx secx?
Answers
Answer:
1. A, E
2. C
Step-by-step explanation:
1. tan theta = 1/cot theta
sec theta = 1/ cos theta
2. Sec^2x-1 = tan^2x
sinx sec x = tanx
= tan^2x/tanx = tan x
The identities are (a) tan(θ) = 1/cot(θ), (c) 1 - sin^2(θ) = cos^2(θ) and (e) sec(θ) = 1/cos(θ) and the simplified form of [tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex] is tan(x)
Part A: The trigonometry identitiesAs a general rule, we have:
tan(θ) = 1/cot(θ)
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
sin^2(θ) + cos^2(θ) = 1
The above means that:
(a) tan(θ) = 1/cot(θ), (c) 1 - sin^2(θ) = cos^2(θ) and (e) sec(θ) = 1/cos(θ) are identities
Part B: The trigonometric proofWe have:
[tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex]
Express the numerator as tan^2(x)
[tex]\frac{\tan^2(x)}{\sin(x)\sec(x)}[/tex]
The product sin(x)sec(x) = tan(x).
So, we have:
[tex]\frac{\tan^2(x)}{\tan(x)}[/tex]
Divide
tan(x)
Hence, the simplified form of [tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex] is tan(x)
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Related Questions
WILL GIVE BRAINLIEST
Which expressions are difference of squares? Select all correct answers.
x2 + y2
x8 - 4
y2 - 25
x2 + 9
(the numbers next to the x's are exponents, i dont know how to write them on here)
Answers
Answer:
I think is x2-y2 cause the number have to be next to
Find the perimeter of the
polygon if ZB = ZD.
5 cm
B
6 cm
D
7 cm
С
P = [?] cm
Enter
Answers
The Perimeter of the polygon is 48 cm.
What is a polygon?A polygon is a closed figure made up of three or more line segments connected end to end.
From the given diagram;
Perimeter of the polygon = AB + BC+ CD + DA
Perimeter of the polygon = 5 + 6 + 6 + 7 + 7 + 6 + 6 + 5
Perimeter of the polygon = 11 + 13 + 13+ 11
The perimeter of the polygon = 48
Hence the Perimeter of the polygon is 48 cm.
Learn more about polygon ;
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The volume of a cube is 365cm3.
Work out the length of its side rounded to 1 DP.
Answers
Answer:
12.4
Step-by-step explanation:
rounded to 1dp
please mark as brainliest if correct
thank you
Answer:
12.4 is the answer.
Step-by-step explanation:
#CarryOnLearningJonny 3/4 collected of a bag of Mardi Gras beads at each parade he attended. He went to 4
different parades. Which two number sentences would tell the total amount of beads collected?
Answers
Answer:
3
Step-by-step explanation:
9b^2=16 solve using Quadratic
Answers
Answer:
[tex]9b^2=16\\b^2=\frac{16}{9} \\\b=\frac{4}{3}[/tex]
Answer:
±4/3
Step-by-step explanation:
9b² = 16
b² = 16/9
take square root of each side
b = ±4/3
pleasee help, thank you so much
Answers
Answer:
-2
Step-by-step explanation:
Use the slope formula when given two points
Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
( the x and y values are determined by the given points )
Given the points ( 0 , 5 ) and ( 1 , 3 )
Plug in the x and y values of the given points into the formula
( remember y values on top x values on bottom )
[tex]slope=\frac{5-3}{0-1} \\5-3=2\\0-1=-1\\slope=\frac{2}{-1} =-2[/tex]
Hence, the answer is D
The graph of y = x 2 is changed to y = x 2 - 3. How does this change in the equation affect the graph?
Answers
Answer:
Brings the Line down 3
Academy sporting goods store sells two different models of a popular
fitness tracker. In one month the store sold 42 trackers for a total of
$6574. Model A costs $127 and Model B costs $189. How many of
each type of tracker was sold?
please help !! i need this done by today !!!!!! its applying systems and i suck at word problems !!
Answers
Answer:
I SUCK AT WORD PROBLEMS TOOOO LOL
Step-by-step explanation:
Please help me ASAP!!
Answers
Answer:
n = 6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
you can create this proportion:
18/n = n/6
cross-multiply:
n² = 108
n = [tex]\sqrt{108}[/tex]
[tex]\sqrt{108}[/tex] = [tex]\sqrt{4}[/tex]·[tex]\sqrt{9}[/tex]·[tex]\sqrt{3}[/tex] = 2·3·[tex]\sqrt{3}[/tex] or 6[tex]\sqrt{3}[/tex]
Last month a bakery sold a total of 3,500 cookies and cupcakes. They sold cookies for $0.75 each and cupcakes for $2 each. If the total sales last month was $4,500, how many cookies and how many cupcakes did the bakery sell?
Answers
Answer:
Number of cookies sold is 2000 and number of cupcakes sold is 1500
Step-by-step explanation:
Let number of cookies be [tex]x[/tex]
and number of cupcakes be [tex]y[/tex] so
[tex]x+y=3500[/tex]
Cost of one cookie is $0.75
Cost of one cupcake is $2
[tex]0.75x+2y=4500[/tex]
[tex]x+y=3500[/tex] [tex]\times 2[/tex]
[tex]2x+2y=7000[/tex]
[tex]-1.25x=-2500\\\Rightarrow x=\dfrac{2500}{1.25}\\\Rightarrow x=2000[/tex]
[tex]y=3500-x=3500-2000\\\Rightarrow y=1500[/tex]
Number of cookies sold is 2000 and number of cupcakes sold is 1500.
Help me. Do not send links or fake answer if not I will report you. The photo will be above¡ Thanks♡
Answers
Answer:
$0.00 $1.00 $1.50 $4.50
Step-by-step explanation:
Hey can you help me fast!!!
Answers
Answer:
A
Step-by-step explanation:
-5(2) + (-5)(1/16)
Samuel earns $50.75 each week by working at a part-time job. He works the same amount of time each day for 5 weeks. What is the total amount of money Samuel earns during the 5-week period?
Answers
Answer:
$253.75
Step-by-step explanation:
He earns $50.75/week. Do 50.75 x 5 = $253.75
A population of 2200 beetles is too large to sustain and decreases in population each
month at a rate of 5%. How would you write your growth rate, b?
Answers
Answer:
2200-b(5) ?
I'm not 100% but here's my 2 cents
10 points, thank you in advance :)
Answers
Answer:
-3 + 10i
sqrt-100 = sqrt100i
sqrt100 = 10
So,
-3 + 10i
PLEASE HELP ME!!!
Tim is sorting his book collection into groups. He places each group onto bookshelves that can each hold a maximum of 25 pounds. His collection includes hardcover books that weigh 3 pounds each and softcover books that weigh 2 pounds each.
Select all of the possible numbers of hardcover books that could be on one bookshelf.
3
4
8
9
12
Answers
Answer:
3 and 4
Step-by-step explanation:
The number of hardcover books will be 3,4, and 8.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tim is sorting his book collection into groups. He places each group onto bookshelves that can each hold a maximum of 25 pounds. His collection includes hardcover books that weigh 3 pounds each and softcover books that weigh 2 pounds each.
Total weight = 25 pounds
The number of hardcover books which weigh less than 25 pounds is,
3 x 3 pounds = 9 pounds
4 x 3 pounds = 12 pounds
8 x 3 pounds =- 24 pounds
Therefore, the number of hardcover books will be 3,4, and 8.
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Which rule describes the composition of transformations that maps triangle BCD to triangle B""C""D""?
Answers
Answer:
(d)
Step-by-step explanation:
Given
See attachment for [tex]\triangle BCD[/tex] and [tex]\triangle B"C"D"[/tex]
Required
The transformations
Using B and B"" as points of reference, we have:
[tex]B = (1,4)[/tex]
[tex]B"" = (5,-1)[/tex]
The transformation is as follows:
First, reflect across y axis.
The rule is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]B(1,4) \to B'(-1,4)[/tex]
Next, translate 6 units right.
The rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex]B' (-1,4) \to B"(-1 + 6,4)[/tex]
[tex]B' (-1,4) \to B"(5,4)[/tex]
Lastly, translate 5 units down
The rule is:
[tex](x,y) \to (x,y-5)[/tex]
So, we have:
[tex]B"(5,4) \to (5,4-5)[/tex]
[tex]B"(5,4) \to (5,-1)[/tex]
Hence; (d) is correct
There are 5 blue, 4 red, 6 magenta, and 3 yellow chips in a bag. One chip is selected at random and then a second is chosen without replacement. Find the probability that the second event will occur.
a) The second was red given that the first was blue.
b) The second was yellow given the first was magenta.
c) The second was green given that the first was red.
d) The second was red given the first was not red.
Answers
Answer:
Step-by-step explanation:
River City Middle School has a weekly contest. The prize is a season pass
to the city amusement park. This week's contest is to guess the number
of lemon jellybeans in a jar of 800 jellybeans. Gerald counted in 3
different sections on the outside of the jar. Here are his results:
5 lemon jelly beans out of 30 jellybeans.
4 lemon jelly beans out of 22 jellybeans.
2 lemon jelly beans out of 12 jellybeans.
based on his sampling, how many lemon jellybeans should he guess are in the jar? Show the mathematics you used to support your answer !
PLEASE HELP
Answers
Answer:
150 lemon jellybeans
Step-by-step explanation:
Add the ratios up to get 12 lemon jelly beans out of 64 jellybeans.
[tex]\frac{12}{64} =\frac{x}{800}[/tex]
Cross multiply:
9600 = 64x
---> x = 150 lemon jellybeans
Sara has 45 comic books. Each month
her collection of novels triples. Write
an expression that represents the
number of comic books she has, y, as
a function of months, X
Answers
this is because she starts with 45 and it triples every month so is u times 3 by the month number and then multiply that by 45 you’ll get ur answer every month
x + 2y = 5
y = 6x + 3
Answers
Answer:
x = −1/13 and y = 33/13 or 2 7/13
Step-by-step explanation:
x+2y=5
x+2(6x+3)=5
x+12x+6=5
13x+6=5
-6 -6
13x= -1
/13 /13
x= -1/13
y=6x+3
y=6(-1/13)+3
y= 33/13
y= 2 7/13
Rectangle A has area 50 cm 2 and length 10 cm. The area of rectangle B is one-half the
area of rectangle A. The rectangles have the same length.
What is the width of rectangle B?
Answers
Answer:
2.5
Step-by-step explanation:
Area of A is 50 cm ^2
length of A is 10
Area of B is 50/2 cm^2 or 25cm^2
area for all rectangles is length * width
so area of B divided by length of b is width of b
25/10 = 2.5
width of b is 2.5
HELPPP If _ABD and ZACD are both right angles, CD = 15, and BD = 4x-9, what is the value
of x?
Answers
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]BD[/tex]≅[tex]CD[/tex]
[tex]4x-9=15[/tex]
[tex]4x=15+9[/tex]
[tex]4x=24\\[/tex]
[tex]x=6[/tex]
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hope it helps....
have a great day!!
what is the taxi fare travel Rs.14 in the begining and then after 5 kilometre at the rate of Rs.38 per kilometre
Answers
the taxi fare travel rs.14=2 kilometer
3 metal cubes that sit next to each other have sides of 5 yards are next to each other. How much total stuff can fit into the cubes?
Answers
Answer:
375[tex]yd^{2}[/tex]
Step-by-step explanation:
Simplify the expression to a polynomial in standard form: (4x-9)(2x^2+2x+1)
Answers
Answer:
8x^3-10x^2-14x-9
Step-by-step explanation:
Answer:
8x^3 - 10x^2 - 14x - 9
Step-by-step explanation:
19. There are 3 roses in a bouquet of assorted flowers. The roses represent 5 15% of the bouquet. How many flowers are in the bouquet? flowers (do not enter label)
Answers
Simplify the expression. Write your answer as a power.
Answers
Answer:
h^7
Step-by-step explanation:
Its just adding another power.
Answer: h^7
Step-by-step explanation: I'm pretty sure! if not thats my bad
help pls! I will mark u brainliest if its correct. but pls dont put one of those links.. ty
Answers
This is a rectangular prism,
Here length = 16 m
Width = 6 m
Height = 3 m
Surface area of rectangular prism = 2( bl + lh + hb )
Where,
b – base length of the rectangular prism.
l – base width of the rectangular prism.
h – height of the rectangular prism.
Putting these values, surface area = 2(16×6 + 16×3+ 3×6)
= 2( 96+48+18) = 2×162 = 324m
hope you get it well :)
100 points / i suck at this
Alison runs a mile in 5 minutes and 50 seconds. Elizabeth runs a mile in 6 minutes and 40 seconds. What is the ratio of Alison's time to Elizabeth's time?
a) 7:8
b) 5.5:6.4
c) 55:64
d) 8:7
Answers
Answer:
7:8
Step-by-step explanation:
First, convert their times to common units. You'll want to put it in seconds:
5 minutes and 50 seconds = 350 seconds
- multiply 5 minutes by 60 to get it into seconds and then add the other 50 seconds to it
- for Elizabeth's time, multiply 6 by 60 seconds and add 40 to it
To get the ratio of their times, divide Alison's time by Elizabeth's time:
350 ÷ 400 = 7:8
Answer:
a) 7:8
Step-by-step explanation:
Alison: 5 minutes and 50 seconds = 355 seconds
Elizabeth: 6 minutes and 40 seconds = 400 seconds
355:400, reduces to 71:80 or 7:8