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Problem 59 Hard Difficulty

(a) Graph the two functions $y=\sin x$ and $y=\sin (\sin x)$ in the standard viewing rectangle. Then for a closer look, switch to a viewing rectangle extending from 0 to $2 \pi$ in the $x$ -direction and from $-1$ to 1 in the $y$ -direction. Compare the two graphs; write out your observations in complete sentences.
(b) Use the graphing utility to estimate the amplitude of the function $y=\sin (\sin x)$
(c) Using your knowledge of the sine function, explain why the amplitude of the function $y=\sin (\sin x)$ is the number sin $1 .$ Then evaluate $\sin 1$ and use the result to check your approximation in part (b).

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

so far apart You can see the crafts are here and on this craft the black car is the graph for wise equal do sine x and the red curve You see here is the graph for bicycle tube signed off sine X. So for part being, what you want to do is we're gonna compare the photographs so far. Thing is, the courts have period to play. And the second thing we see is that amplitude Oh, why is equal to sign X? He's, uh, one. When asked the aptitude off. Why is he going to sign off? Sliding off its is approximately zero point eight. For what? So that's why you cannot be compared to Gratz Now, For part C, we have sign off X. It ranges between negative one and positive one. Therefore, sign off sine X where the maximum when sign X he close. What? So therefore d aptitude off. Why is he going to sign up? Sine X is sign off. Sign off high over to which is sign off. What? So then using the rap using calculator we can actually find that sign of one is approximately 0.841 and you can actually see that the graph as well

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor