Use one of the identities cos(t+2 πk)=cost or sin(t+2 πk)=sint to evaluate each expression. (a)

Name: Problem 41, Chapter 7: Precalculus
Uploaded: 2020-08-01T17:38:51-08:00
Duration: 2 min 2 s
Channel: Bobby Barnes
Description: Use one of the identities cos(t+2 πk)=cost or sin(t+2 πk)=sint to evaluate each expression. (a) cos((π)/(4)+2 π) (b) sin((π)/(3)+2 π) (c) sin((π)/(2)-6 π)

step 1 They want us to use those two identities up top there to help us solve these equations. So let's

Question

Use one of the identities $\cos (t+2 \pi k)=\cos t \operatorname{or} \sin (t+2 \pi k)=\sin t$ to evaluate each expression. (a) $\cos \left(\frac{\pi}{4}+2 \pi\right)$ (b) $\sin \left(\frac{\pi}{3}+2 \pi\right)$ (c) $\sin \left(\frac{\pi}{2}-6 \pi\right)$

   Use one of the identities $\cos (t+2 \pi k)=\cos t \operatorname{or} \sin (t+2 \pi k)=\sin t$ to evaluate each expression.
(a) $\cos \left(\frac{\pi}{4}+2 \pi\right)$
(b) $\sin \left(\frac{\pi}{3}+2 \pi\right)$
(c) $\sin \left(\frac{\pi}{2}-6 \pi\right)$

Precalculus

David Cohen,… 4th Edition

Chapter 7, Problem 41

Instant Answer

Solved by Expert Bobby Barnes

08/01/2020

Step 1

This means that adding any multiple of $2\pi$ to the angle does not change the value of the cosine function. Show more…

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Use one of the identities $\cos (t+2 \pi k)=\cos t \operatorname{or} \sin (t+2 \pi k)=\sin t$ to evaluate each expression. (a) $\cos \left(\frac{\pi}{4}+2 \pi\right)$ (b) $\sin \left(\frac{\pi}{3}+2 \pi\right)$ (c) $\sin \left(\frac{\pi}{2}-6 \pi\right)$

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Key Concepts

Angle Reduction in Trigonometry

Angle reduction involves rewriting an angle by adding or subtracting full rotations (multiples of 2?) to obtain an equivalent angle within a standard range. This method simplifies the evaluation of trigonometric functions by reducing the angle to a more familiar or manageable value.

Periodicity of Trigonometric Functions

Trigonometric functions such as sine and cosine are periodic, meaning they repeat their values over regular intervals. Specifically, the sine and cosine functions have a period of 2?, which implies that adding or subtracting any integer multiple of 2? to the input angle does not change the output of the function.

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