Find all angles of theta where 0° ≤ 𝜃 < 360°, with the given functions

Question

cos 𝜃 = 0.34

tan 𝜃 = 4.13

Answer 1

To answer this question, you must be familiar with the unit circle. To find one of the angles, plug into your calculator cos^-1(0.34) and you will get 70.123°. That's the angle shown here:

But there is a second angle with the cos of 0.34 shown here at -70.123° aka 289.877°

The same holds true for tan 4.13. The calculator tells you the angle is 76.389° but adding 180° will also get you the same tangent.

So cos(θ) = 0.34 holds for θ = 70.123° and 289.877° and tan(θ) = 4.13 holds for θ = 76.389° and 256.389°

Try it by typing cos(70.123°) and cos(289.877°) as well as tan(76.389°) and tan(256.389°)