Manipulating trig expressions with pythagorean identities

The  exercise appears under the Trigonometry Math Mission. This exercise practices the Pythagorean identities from trigonometry by having students manipulate expressions with these identities.

Types of Problems
There is one type of problem in this exercise:


 * 1) Manipulate the expression: This problem presents a trigonometric expression with squares of trigonometric functions. The student is expected to use identities to manipulate the expression into an alternative form from a multiple choice list.Mtewpi1.png

Strategies
Knowledge of Pythagorean, reciprocal, and quotient identities are encouraged to ensure success on this exercise.
 * 1) The quotient identities are used to write tangent and cotangent in terms of sine and cosine.
 * 2) The reciprocal identities connect trigonometric functions with their reciprocals.
 * 3) The vital Pythagorean identity states that sin^2(theta)+cos^2(theta)=1. This particular identity can be itself manipulated into any other Pythagorean identity by reciprocals and quotients.

Real-life Applications

 * 1) Manipulation of trigonometric expressions is important for being able to prove identities and solve equations with trigonometric functions.
 * 2) Trigonometry itself has several applications in physics regarding motion.