### All Precalculus Resources

## Example Questions

### Example Question #1 : Angles In The Coordinate Plane

Convert radians to degrees.

**Possible Answers:**

**Correct answer:**

Write the conversion factor between radians and degrees.

Cancel the radians unit by using dimensional analysis.

### Example Question #2 : Angles In The Coordinate Plane

Convert to degrees.

**Possible Answers:**

**Correct answer:**

Write the conversion factor of radians and degrees.

Substitute the degree measure into .

### Example Question #3 : Angles In The Coordinate Plane

Determine the angle in degres made in the plane by connecting a line segment from the origin to .

Assume

**Possible Answers:**

**Correct answer:**

Firstly, since the point is in the 3rd quadrant, it'll be between and . If we take to be the horizontal, we can form a triangle with base and leg of values and . Solving for the angle in the 3rd quadrant given by ,

Since this angle is made by assuming to be the horizontal, the total angle measure is going to be:

### Example Question #4 : Angles In The Coordinate Plane

Find the degree measure of radians. Round to the nearest integer.

**Possible Answers:**

**Correct answer:**

In order to solve for the degree measure from radians, replace the radians with 180 degrees.

The nearest degree is .

### Example Question #5 : Angles In The Coordinate Plane

Given a triangle, the first angle is three times the value of the second angle. The third angle is . What is the value of the second largest angle in degrees?

**Possible Answers:**

**Correct answer:**

A triangle has three angles that will add up to degrees.

Convert the radians angle to degrees by substituting for every .

The third angle is 60 degrees.

Let the second angle be . The first angle three times the value of the second angle is . Set up an equation that sums the three angles to .

Solve for .

Substitute for the first angle and second angle.

The second angle is:

The first angle is:

The three angles are:

The second highest angle is: