# How would you convert f(x) = 20sin(π/6(t)) + 4 into a cosine function?

Jan 2, 2017

$f \left(x\right) = 20 \cos \left(\frac{\pi}{6} \left(3 - t\right)\right) + 4$

#### Explanation:

To convert f(x)=20sin(π/6(t))+4 into cosine function, we can use the identity

$\cos \left(\frac{\pi}{2} - A\right) = \sin A$

Hence sin(π/6(t))=cos(pi/2-π/6(t))

= $\cos \left(\frac{\pi}{6} \left(3 - t\right)\right)$

Hence $f \left(x\right) = 20 \cos \left(\frac{\pi}{6} \left(3 - t\right)\right) + 4$