§2.2 The sine and cosine functions

Introduction

The sine and cosine functions

Which of the following is the derivative of the cosine function, that is $\frac{d}{dx}[\cos(x)]$?

Let $h(t) = 3\cos(t) - 4\sin(t)$. Which expression is $\frac{dh}{dt}$?

The island population $P(t) = 24 + 8\sin(t)$ is measured in hundreds with $t$ in decades since 2010. The quantity $P'(2) \approx -3.329$ tells us that on January 1, 2030 the population is

For $f(x) = 2x + \frac{\sin(x)}{2}$, compute the exact slope of the tangent line at $x = \frac{\pi}{6}$ as a decimal rounded to three places.

For $p(z) = z^4 + 4^z + 4\cos(z) - \sin(\frac{\pi}{2})$, compute $p'(0)$ rounded to three decimals.

The slope of the tangent line to $y = \sin(x)$ at $x = 0$ equals $1$.