Lesson 8 “Sine”ing and “Cosine”ing It Solidify Understanding

Ready

Rewrite each fraction in an equivalent form by performing any indicated operation and rationalizing the denominators, when appropriate.

1.

$\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}$

2.

$\frac{\frac{8 \sqrt{3}}{5}}{\frac{1}{5}}$

3.

$\frac{8}{\frac{1}{2}}$

4.

$\frac{\frac{7 \sqrt{3}}{2}}{\frac{1}{2}}$

5.

$\frac{1}{\sqrt{2}}$

6.

$\frac{3}{\sqrt{3}}$

7.

$\frac{4}{\sqrt{8}}$

8.

$\frac{\frac{2}{3}}{\frac{1}{2}}$

9.

$\frac{\frac{2}{\sqrt{7}}}{\frac{5}{\sqrt{7}}}$

Set

10.

Triangle $A B C$ is an isosceles right triangle. The length of one side is given. Fill in the values for the missing sides and angles $A$ and $B$ .

11.

Each point on the circle marks the end of a terminal ray in standard position. Label the measure of the angle of rotation at each position of the terminal ray. Angles will be in radians. Leave $π$ in your answer. (Each section is equal.)

12.

Use the values in #11 to write the exact coordinates of the points on the circle. Be mindful of the numbers that are negative.

13.

Find the arc length, $s$ , from the point $(1, 0)$ to each point around the circle. Record your answers as decimal approximations to the nearest thousandth.

Use your calculator to find the following values.

14.

$\sin \frac{5 π}{4} =$

15.

$\sin \frac{7 π}{4} =$

16.

Why are both of your answers negative?

17.

$\cos \frac{π}{4} =$

18.

$\cos \frac{7 π}{4} =$

19.

Why are both of your answers positive?

20.

$\sin \frac{3 π}{4} =$

21.

$\cos \frac{3 π}{4} =$

22.

Why is one answer positive and one answer negative?

Go

Graph the equation. Plot $3 points$ on the midline and plot a minimum and a maximum point. Use these points to sketch at least two periods of the graph.

23.

$f (x) = 2 \cos (5 x)$

24.

$g (x) = - 3 \cos 9 x + 2$

25.

$h (x) = - 5 \cos (18 x) - 3$

26.

$k (x) = 15 \sin (30 x) + 6$