### All Precalculus Resources

## Example Questions

### Example Question #1 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Find angle A of the following triangle:

**Possible Answers:**

None of the other answers

**Correct answer:**

We are given the hypotenuse and the side opposite of the angle in question. The trig function that relates these two sides is SIN. Therefore, we can write:

In order to solve for A, we need to take the inverse sin of both sides:

which becomes

### Example Question #2 : Inverse Sine And Cosine Functions

Consider , where theta is valid from . What is a possible value of theta?

**Possible Answers:**

**Correct answer:**

Solve for theta by taking the inverse sine of both sides.

Since this angle is not valid for the given interval of theta, add radians to this angle to get a valid answer in the interval.

### Example Question #1 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Evaluate:

**Possible Answers:**

**Correct answer:**

First evaluate .

To evaluate inverse cosine, it is necessary to know the domain and range of inverse cosine.

For:

The domain is only valid from .

is only valid from .

The part is asking for the angle where the x-value of the coordinate is . The only possibility on the unit circle is the second quadrant.

Next, evaluate .

Using the same domain and range restrictions, the only valid angle for the given x-value is in the first quadrant on the unit circle.

Therefore:

### Example Question #4 : Inverse Sine And Cosine Functions

Evaluate:

**Possible Answers:**

**Correct answer:**

To find the correct value of , it is necessary to know the domain and range of inverse cosine.

Domain:

Range:

The question is asking for the specific angle when the x-coordinate is half.

The only possibility is located in the first quadrant, and the point of the special angle is

The special angle for this coordinate is .

### Example Question #1 : Evaluate Expressions That Include The Inverse Sine Or Cosine Function

Find the value of .

**Possible Answers:**

**Correct answer:**

In order to determine the value or values of , it is necessary to know the domain and range of the inverse sine function.

Domain:

Range:

The question is asking for the angle value of theta where the x-value is under the range restriction. Since is located in the first and fourth quadrants, the range restriction makes theta only allowable from . Therefore, the theta value must only be in the first quadrant.

The value of the angle when the x-value is is degrees.

### Example Question #6 : Inverse Sine And Cosine Functions

Find the inverse of the function

.

Make sure the final notation is only in the forms including , , and .

**Possible Answers:**

**Correct answer:**

The easiest way to solve this problem is to simplify the original expression.

To find its inverse, let's exchange and ,

Solving for

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