Applying angle addition formulas

The  exercise appears under the Trigonometry Math Mission. This exercise practices the angle addition formula in various contexts.

Types of Problems
There are three types of problems in this exercise:


 * 1) Use the picture to understand angle addition: This problem has a labeled diagram that can be used to find a particular trigonometric value using an angle addition formula. The student is expected to use this law to find the correct expression and write it in the space provided.Aaaf1.png
 * 2) Write the double angle formula using angle addition: This problem asks for the value of a double angle expression. The student is expected to use the angle addition laws to discover the double angle formulas.Aaaf2.png
 * 3) Find the value of a trig function: This problem asks for the value of a trigonometric function at a non-unit circle value. The student is expected to use the angles addition formulas to find the correct value and write it in the space provided.Aaaf3.png

Strategies
Knowledge of the angle addition formulas, half-angle formulas, and the double angle formulas are encouraged beforehand to ensure success on this exercise.
 * 1) The sine addition formulas are $$ sin(x\pm y)=sin(x)cos(y)\pm cos(x)sin(y)$$.
 * 2) The cosine addition formulas are $$ cos(x\pm y)=cos(x)cos(y)\mp sin(x)sin(y)$$.
 * 3) To prove the double angles, find the angle sum of (x+x) since x+x=2x.

Real-life Applications

 * 1) The problems in this exercises are, in general, applications of the formulas.
 * 2) Trigonometry itself has several applications in physics regarding motion.