Question

Rewrite y = 3sin(1/3x+pi/2) as a cosine

Answer 1

To rewrite the equation \( y = 3\sin\left(\frac{1}{3}x + \frac{\pi}{2}\right) \) as a cosine function, we can use the sine to cosine phase shift identity. The sine function can be expressed in terms of cosine as follows:

\[
\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)
\]

In this case, let \( \theta = \frac{1}{3}x \). Then we have:

\[
\sin\left(\frac{1}{3}x + \frac{\pi}{2}\right) = \cos\left(\frac{1}{3}x\right)
\]

Now, we can substitute this back into the original equation:

\[
y = 3\sin\left(\frac{1}{3}x + \frac{\pi}{2}\right) = 3\cos\left(\frac{1}{3}x\right)
\]

Thus, the rewritten equation in terms of cosine is:

\[
y = 3\cos\left(\frac{1}{3}x\right)
\]