Question

Find the value for tan θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form

Find the value for sec θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.

Answer 1

Explanation:

The point (-3, 4) is in QII. If we plot this point and drop an altitude then connect the point to the origin, we have a right triangle with side opposite measuring 4 units and side adjacent measuring |-3|. The tangent of the reference angle is the ratio side opposite/side adjacent, so

`tan\theta=-(4)/(3)`

Since secant is the reciprocal of cosine, let's find the cosine of the reference angle and then flip it upside down. The cosine of the angle is the side adjacent (got it) over the hypotenuse (don't have it). We can find the hypotenuse using Pythagorean's Theorem:

`c^2=-3^2+4^2` s0

`c^2=25` and

c = 5

The cosine of the angle theta is

`cos\theta=-(3)/(5)`; therefore,

`sec\theta=-(5)/(3)`