What is the measure of each of these four angles?

Question

1. A reference angle of 82˚ is used to construct 4 angles in a coordinate plane, with 1 angle per quadrant, where all of the angles have a positive measure less than 60 degrees. In keeping in mind the requirement of showing the steps you took to calculate the answers, what are the measures of each of the angles below, filling in the blank?
2. The angle in Quadrant I is _______˚;
3. The angle in Quadrant II is ________˚;
4. The angle in Quadrant III is ________˚;
5. The angle in Quadrant IV is ________˚.
6. Find tan(θ) to four decimal places provided that sin(θ) is equal to 2/9.

Answer 1

The question has a typo. It's really "all the angles have a measure less than 360 degrees."

The reference angle is distance from the x axis.

Q1: 80 degrees.

Q2: 180 - 80 = 100 degrees.

Q3: 180 + 80 = 260 degrees.

Q4: 360 - 80 = 280 degrees.

sin is opposite/hypotenuse = 2/9.

tan is opposite/adjacent.

Find adjacent by using Pythagorean theorem.

2^2 + x^2 = 9^2

4 + x^2 = 81

x^2 = 77

x = sqrt(77)

tanx = 2/sqrt(77) = 2*sqrt(77)/77 = approximately .2279

Answer 2