This document discusses trigonometric ratios and their use in solving for angles in a right triangle. It provides an example triangle with sides of 10, 10, and 14.14 units and uses the trigonometric ratios of sine, cosine, and tangent to calculate the measure of the angle φ as being 45 degrees.

1. V2 = -3V 0
I
θ = 0˚
0 I
V1 = 2V

2. adjacent
cosine ϕ = hypotenuse
4
= 5.657
= 0.707

3. X = 10
ϕ
Y = -10

4. sin ϕ = opposite / hypotenuse ( 10 ÷ 14.14 = 0.707) sin -1 = 450
cos ϕ = adjacent / hypotenuse ( 10 ÷ 14.14 = 0.707) cos -1 = 450
tan ϕ = opposite / adjacent ( 10 ÷ 10 = 1) tan -1 = 450