Trigonometry : Identities of Inverse Operations

Example Questions

Example Question #61 : Trigonometry

Simplify using identities. Leave no fractions in your answer.       Explanation:

The easiest first step is to simplify our inverse identities: Cross cancelling, we end up with Finally, eliminate the fraction: Thus, Example Question #1 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.

1.      Explanation:

Using the quotient identities for trig functions, you can rewrite, and Then the fraction becomes Example Question #69 : Trigonometry

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.      Explanation:

Use the Pythagorean Identities: and Thus the expression becomes, .

Example Question #1 : Identities Of Inverse Operations

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.      Explanation:

Use the distributive property (FOIL method) to simplify the expression.   Using Pythagorean Identities: .

Example Question #71 : Trigonometry

Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.      Explanation:

First, simplify the first term in the expression to 1 because of the Pythagorean Identity. Then, simplify the second term to .

This reduces to .

The expression is now, .

Distribute the negative and get, .

Example Question #72 : Trigonometry

Solve each question over the interval       Explanation:

Divide both sides by to get .

Take the square root of both sides to get that and .

The angles for which this is true (this is taking the arctan) are every angle when and .

These angles are all the multiples of Example Question #74 : Trigonometry can be stated as all of the following except...      Explanation:

Let's look at these individually: is true by definition, as is . is also true because of a co-function identity.

This leaves two - and we can tell which of these does not work using the fact that , which means that is our answer.

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