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

820,000 is the answr

Answer from: Quest

Answerthe simplified expression is $2x + 28$ explanationthe given expression is, $2(10) + 2(x - - 4)$ let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes, $2(10) + 2(x + 4)$ we now expand the parenthesis to get, $20 + 2x + 8$ we group like terms to obtain, $2x + 8 + 20$ this simplifies to, $2x + 28$

Another question on Mathematics

Mathematics, 21.06.2019 17:30

The length of triangle base is 26. a line, which is parallel to the base divides the triangle into two equal area parts. find the length of the segment between triangle legs.

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Af jewelry box is in the shape of a rectangular prism with an area of 528 cube inches. the length of the box is 12 inches and the height is 5 1/2 inches. what is the width of the jewelry box

Answers: 1

Answer

Mathematics, 22.06.2019 02:20

Two researchers are attempting to create a new psychotherapy protocol that more reduces panic attacks. they believe that they have succeeded and are now in the clinical trial period of their protocol's development. they are working with several cohort groups, some of which have been through the new protocol, while others have done the standard protocol currently recommended. if these researchers are interested in evaluating the difference in the percentage of test subjects who successfully decreased their panic attacks in 2 months on the new protocol versus the percentage of test subjects who successfully decreased their panic attacks in 2 months with the traditional protocol, which of the following statistical tests would be most appropriate? a. analysis of variance (anova) b. correlation c. chi-square test d. paired t-test e. independent t-test

Answers: 2

Answer

Mathematics, 22.06.2019 04:20

Find a conversion factor between square centimeters and square meters. write it in three forms. square centimeters = 1 square meter

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