CPM Homework Help : PCT Problem 4-24

Find the following values using special right triangles (give exact values). Do not use your unit circle, except to check.

$\text{sin }\frac { 4 \pi } { 3 }$

$\text{cos }\frac { 11 \pi } { 3 }$

$\text{sin }( - \frac { 5 \pi } { 6 } )$

$\text{cos }( - \frac { 2 \pi } { 3 } )$

Compute without a calculator

Hint (a):

1. Draw circle and locate the angle. Circle with dashed, horizontal diameter, 5 green points located as follows: on left & right ends of diameter, at center of circle, & 2 points equally spaced, on top half. Blue point on the lower left quarter of the circle.

Show 1(a):

2. Draw a right triangle whose base is the $x$ -axis. Added: right triangle in fourth quadrant: horizontal leg, on the negative, x axis, hypotenuse, from center of circle to blue point.

Show 2(a):

3. Label side lengths. Labels added: horizontal leg, negative 1 half, vertical leg, negative 1 half times square root of 3.

Show 3(a):

4. Choose the $y$ -value for the sine!

Circle with dashed, horizontal diameter, 5 green points located as follows: on left & right ends of diameter, at center of circle, & 2 points equally spaced, on top half. Blue point on the lower left quarter of the circle.

Added: right triangle in fourth quadrant: horizontal leg, on the negative, x axis, hypotenuse, from center of circle to blue point.

Labels added: horizontal leg, negative 1 half, vertical leg, negative 1 half times square root of 3.