Question

Tan of theta?

Answer 1

tan = opposite/adjacent, by definition.

Answer 2

Can you find sine of theta?

Answer 3

In this case the opposite and adjacent are both -3. The hypotenuse, r, can be found with Pythagoras.

Alternatively, since the legs of the triangle are equal we know the reference angle is 45° or π/4. And since it lies in the third quadrant the sine and cosine are both negative and the tangent is positive.

Answer 4

Tan θ =y/x=1. θreference=pi/4 or 45°. θ=pi+pi/4=5pi/4 or 180+45=225°

Answer 5

first principles, tangent = opp/adj