CPM Homework Help : PC Problem 4-25

Given: $\text{cos }θ =\frac { 3 } { 5 }$ .

Draw a right triangle and place values on the sides so that $\text{cos }θ =\frac { 3 } { 5 }$ .
Draw a unit circle diagram to clearly show the TWO possible positions for $θ$ .
Use the Fundamental Pythagorean Identity or a right triangle to find all possible values for $\text{sin }θ$ .
Find all possible values for $\text{tan }θ$ .

Drawing (a):

Drawing (b):

Right triangle labeled as follows: Horizontal leg, 3, hypotenuse, 5, angle opposite vertical leg, theta.

Right triangle is placed in unit circle with top vertex in first quadrant, shaded blue, a reflection of the triangle across the x axis, places a second right triangle with bottom vertex in fourth quadrant, shaded purple.

Hint (c):

It must be a $3-4-5$ triangle because of the Pythagorean Theorem. Determine the two sine values.

Answer (d):

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\pm4}{3}=\pm\frac{4}{3}$