Question

The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Answer 1

Draw the angle on a x y coordinate plane, with the first line traveling from origin (0,0) to (1,0) and the second line traveling from origin (0,0) to (1,-1), then connect point (1,0) to point (1,-1) and you have your triangle.
Because a^2+ b^2 = c^2 (Pythagorean theorem) and we know a = 1 and b =1, and as 1^2 + 1^1 = c^2 which is √2 we can now figure out our angles!
If the origin is the angle θ, then sinθ= opposite/hypotenuse which is 1/√2 which is often simplified as √2/2. Knowing this, can you find the rest of the angles?

Answer 2

The Unit Circle is your friend!