GRE Subject Test: Math : Sine

Example Questions

Evaluate:       Explanation:

Evaluating this integral requires use of the "Product to Sum Formulas of Trigonometry":

For: So for our given integral, we can rewrite like so: This can be rewritten as two separate integrals and solved using a simple substitution. Solving each integral individually, we have:  Substituting this into the integral results in: The other integral is solved the same way:  Substituting this into the integral results in: Now combining these two statements together results in one of the answer choices: Evaluate:       Explanation:

This integral can be easily evaluated by following the rules outlined for integrating powers of sine and cosine.

But first a substitution needs to be made:   Now that we've made this substitution, we will use the rules outlined for integrating powers of sine and cosine:

In General: 1. If "m" is odd, then we make the substitution , and we use the identity .

2. If "n" is odd, then we make the substitution , and we use the identity .

For our given problem statement we will use the first rule, and alter the integral like so:     Now we need to substitute back into v: Now we need to substitute back into u, and rearrange to make it look like one of the answer choices: Example Question #3 : Trigonometric Functions

Find       Explanation:

Step 1: Draw a triangle..

The short sides have a length of and the hypotenuse has a length of .

Step 2: Find Sin (Angle A): Step 3: Rationalize the root at the bottom:  All GRE Subject Test: Math Resources 