Angle Sum Formulas for Cosine and Sine

You are going to use the following demo to build intuition about angle sum formulas for cosine and sine. You will also derive the formulas. Start by looking at the figure. What do you notice? What shapes are there?

Focus on right triangle ABC, which has hypotenuse length AB=1. Drag the lengths AC and BC to the triangle.

Focus on right triangle ABE, which has hypotenuse length AB=1. Drag the lengths AE and BE to the triangle.

Focus on right triangle CBD, which has hypotenuse length BC. Drag the lengths BD and CD to the triangle.

Find the measure of angle CAG. (Hint: What is the angle sum of a triangle? Use this on triangles ABE and ABC. Solve!)

Focus on right triangle AGC, which has hypotenuse length AC. Drag the lengths AG and CG to the triangle.

Find the lengths of HA and HB. (Hint: Can you drag the lengths from congruent segments?)

Summarize your answers here by giving the angle sum formulas for cosine and sine in the box below or by dragging the values in the figure below.