CPM Homework Help : PC Problem 4-70

Given $θ =\frac { \pi } { 3 }$ , find the exact value of each of the following trig expressions.

Hint:

Draw a unit circle and label the $x$ and $y$ -coordinates for $θ$ . You can easily find all trig functions once you know the coordinates.

Show Me:

Circle with horizontal diameter, point in first quadrant, about 2 thirds up from right diameter endpoint, right triangle with hypotenuse between center & point, horizontal leg on positive x axis, labeled 1 half, vertical leg labeled 1 half times square root of 3.

$\text{sec }θ$
Answer (a):
$\frac{1}{\text{cos}(\theta)}=\frac{1}{x}=\frac{1}{\frac{1}{2}}=2$

$\text{csc }θ$
Hint (b):
What is the $\text{csc}θ$ in terms of the other trig functions?

$\text{tan }θ$
Hint (c):
What is the $\text{tan}θ$ in terms of the other trig functions?

$\text{cot }θ$
Hint (d):
What is the $\text{cot}θ$ in terms of the other trig functions?