Mathematics, 03.08.2019 19:30 ciaraberger

10. rewrite with only sin x and cos x. (1 point) sin 2x - cos 2x a) 2 sinx cosx - 1 + 2 sin2x b) 2 sin x cos2x - 1 + 2 sin2x c) 2 sin x cos2x - sin x + 1 - 2 sin2x d) 2 sin x cos2x - 1 - 2 sin2x 11. find the exact value by using a half-angle identity. (1 point) sin 22.5° a) negative one half times the square root of quantity two plus square root of two. b) one half times the square root of quantity two plus square root of two. c) negative one half times the square root of quantity two minus square root of two. d) one half times the square root of quantity two minus square root of two 15. verify the identity. (1 point) cot x minus pi divided by two. = -tan x need asap !

Answers: 1

Show answers

Answers

Answer from: kbuhvu

10. Rewrite with only sin x and cos x.
sin 2x - cos 2x

sin2x = 2sinxcosx
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2

sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2

sin2x- cos2x=2sinxcosx-1+2(sinx)^2

the answer is the letter b) 2 sin x cos2x - 1 + 2 sin2x

11. Find the exact value by using a half-angle identity. sin 22.5°Using the half angle formula you get:sin2(θ)=12[1−cos(2θ)]if θ=22.5° then 2θ=45°so you get:sin2(22.5°)=12[1−cos(45°)]sin2(22.5°)=12[1−√2/2]=2−√24and square root both sides:sin(22.5°)=±√2−√24=±0.382so
sin(22.5°)=0.382the answer is the letter D) one half times the square root of quantity two minus square root of two
15. Verify the identity.
cot x minus pi divided by two. = -tan x
Cot(x-pi/2)=-tan(x)
sin(A − B) = sin A cos B − cos A sin B
sin(x – pi/2) = sin x cos (pi/2) − cos x sin (pi/2)=-cosx

cos(A − B) = cos A cos B − sin A sin B
cos(x− pi/2) = cos x cos pi/2 − sin x sin pi/2=-sinx
Cot(x-pi/2)=cos(x-pi/2)/sin(x-pi/2)
= (-sinx)/(-cosx)=-tanxok

Answer from: hollie62

Trigonometric functions can only be applied to right triangles. There are six trigonometric functions. The answer to part 1 is an option (a) and the answer to part 2 is an option (d).

Part (1)

Rewrite with only sin x and cos x.

The given trigonometric expression is $\sin 2x - \cos 2x$ .

Apply the following identities in the given expression and solve them further.

$\begin{aligned}\sin2x&=2\;\rm{sin\;x\;cos\;x}\\\cos2x&=1-2\sin^2x\end{aligned}$

Thus,

$\begin{aligned} \sin 2x - \cos 2x&=2 \sin x \cos x-\left(1-2 \sin^2 x \right)\\&=2 \sin x \cos x-1+2 \sin^2 x\\&=2 \sin^2 x+2 \sin x \cos x-1\end{aligned}$

Hence, option (a) is correct.

Part (2)

Find the exact value by using a half-angle identity.

$\sin 22.5$

Now, we know that,

$\begin{aligned}\cos 2x&=1-2 \sin^2 x\\2 \sin^2 x&=1 -\cos 2x\\\sin^2 x&=\dfrac{1-\cos 2x}{2}\\\sin x&= \sqrt {\dfrac{1-\cos 2x}{2}} \end{aligned}$

From the above question, substitute the value of x=22.5, and solve it further.

$\begin{aligned}\sin 22.5&= \sqrt {\dfrac{1-\cos 2 \times 22.5}{2}}\\&= \sqrt {\dfrac{1-\cos 45}{2}}\\&=\sqrt {\dfrac{1- \dfrac{1}{\sqrt 2}}{2}}\\&=\sqrt{\dfrac{\sqrt2-1}{2 \sqrt 2}}\end{aligned}$

Part (3)

Incomplete question.

To know more about it, please refer to the link:

link

Answer from: Quest

Your pictures are upside down

Answer from: Quest

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the x-axis .

step-by-step explanation:

Which of the following statements best describes the transverse axis of a hyperbola?

Another question on Mathematics

Mathematics, 21.06.2019 20:00

Guys i need ! graded assignment grade 8 checkpoint 2, part 2 answer the questions below. when you are finished, submit this assignment to your teacher by the due date for full credit. total score: of 9 points (score for question 1: of 4 points) 1. the cost of renting a car for a day is $0.50 per mile plus a $15 flat fee. (a) write an equation to represent this relationship. let x be the number of miles driven and y be the total cost for the day. (b) what does the graph of this equation form on a coordinate plane? explain. (c) what is the slope and the y-intercept of the graph of the relationship? explain.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Kayla made observations about the sellin price of a new brand of coffee that sold in the three different sized bags she recorded those observations in the following table 6 is $2.10 8 is $2.80 and 16 is to $5.60 use the relationship to predict the cost of a 20oz bag of coffee.

Answers: 3

Answer

Mathematics, 21.06.2019 21:10

What is the domain of the given function? {(3,-2), (6, 1), (-1, 4), (5,9), (-4, 0); o {x | x= -4,-1, 3, 5, 6} o {yl y = -2,0, 1,4,9} o {x|x = -4,-2, -1,0, 1, 3, 4, 5, 6, 9} o y y = 4,-2, -1, 0, 1, 3, 4, 5, 6, 9}

Answers: 1

Answer

Mathematics, 21.06.2019 22:20

Factor and solve to find roots x squared -x - 90 =0

Answers: 1

Answer

You know the right answer?

10. rewrite with only sin x and cos x. (1 point) sin 2x - cos 2x a) 2 sinx cosx - 1 + 2 sin2x b) 2 s...

Questions

Mathematics, 04.06.2020 19:09

The following table shows the number of comments on each of Omar's 9 99 most recent social media posts....

Mathematics, 04.06.2020 19:09