Christopher S.

Each limit represents the derivative of some function
$f$ at some number $a .$ State such an $f$ and $a$ in each case.
$$
\lim _{h \rightarrow 0} \frac{(1+h)^{10}-1}{h}
$$

Evaluating Trigonometric Functions. find the exact values of the six trigonometric
functions of the angle $\theta$ for each of the two triangles.
Explain why the function values are the same.

Evaluating Trigonometric Functions, sketch a right triangle corresponding to the
trigonometric function of the acute angle $\theta .$ Use the
Pythagorean Theorem to determine the third side and
then find the other five trigonometric functions of $\theta$ .
$$\tan \theta=\frac{3}{4}$$

Evaluating Trigonometric Functions, sketch a right triangle corresponding to the
trigonometric function of the acute angle $\theta .$ Use the
Pythagorean Theorem to determine the third side and
then find the other five trigonometric functions of $\theta$ .
$$\tan \theta=\frac{4}{5}$$

$$
\begin{array}{c}{\text { Evaluating Trigonometric Functions of } 30^{\circ}, 45^{\circ} \text { and }} \\ {60^{\circ} \text { In Exercises } 21-30 \text { , construct an appropriate triangle }} \\ {\text { to find the missing values. }\left(0^{\circ} \leq \theta \leq 90^{\circ}, 0 \leq \theta \leq \pi 2\right)} \\ {\text { Function }\quad \theta(\text { deg }) \quad \theta(\text { rad }) \quad \text { Function Value }}\end{array}
$$
$\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \sin \quad \quad \quad 30^{\circ}$

Using a Calculator, use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct mode.)
$${ (a) }\sin 10^{\circ} \quad \text { (b) } \cos 80^{\circ}$$