Trigonometry – Sum and Difference Formulas for Sine and Cosine for unknown angles

By | September 22, 2016

Sum and Difference Formulas

In this tutorial the students will learn how to use the sum and difference formulas for unknown angles. The students will be given the quadrants and the result of the specified trigonometric functions.  The student will then construct the needed triangles to solve the question.

Key Points of Knowledge

Sum and Difference Formulas

cos (α + β) = cos (α) cos (β) - sin (α) sin (β)

cos (α - β) = cos (α) cos (β) + sin (α) sin (β)

sin (α + β) = sin (α) cos (β) + cos (α) sin (β)

sin (α - β) = sin (α) cos (β) - cos (α) sin (β)

Pythagorean Theorem

a² + b² = c²

Pythagorean Triples

3, 4, 5

5, 12, 13

7, 24, 25 etc...

Quadrants on the Coordinate Plane


Fraction Multiplication

Fraction Addition

More Examples