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 !

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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

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

$i=\frac{85}{100}=0.85$

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

Answer from: Quest

10 you would take 50/ .2

step-by-step explanation:

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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...

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