CPM Homework Help : PC Problem 4-123

Given sin $θ =\frac { 2 } { 3 }$ and $\frac { \pi } { 2 }< θ < \pi$ . Find the values of the $5$ other trigonometric functions.

Hint:

1. Draw a non-unit circle placing in the triangle in the appropriate quadrant.
2. Label/find the sides of the triangle. Don't forget the check the sign.
3. Now the other $5$ trig functions can be easily found from these sides.

Partial Answer:

$x^2 + 2^2 = 3^2$
$x^2 = 5$
$x=\pm\sqrt{5}$
In this case we are in the 2nd quadrant so it must be negative.
Circle with horizontal & vertical diameters, right triangle, hypotenuse from center of circle to point in second quadrant, labeled 3, horizontal leg on negative x axis, labeled negative square root of 5, vertical leg labeled 2, central angle labeled theta.