### All High School Math Resources

## Example Questions

### Example Question #1 : Trigonometry

If the polar coordinates of a point are , then what are its rectangular coordinates?

**Possible Answers:**

**Correct answer:**

The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)

The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.

In this problem, the polar coordinates of the point are , which means that and . We can apply the conversion formulas to find the values of x and y.

The rectangular coordinates are .

The answer is .

### Example Question #2 : Trigonometry

What is the ?

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Trigonometry

In the right triangle above, which of the following expressions gives the length of y?

**Possible Answers:**

**Correct answer:**

is defined as the ratio of the adjacent side to the hypotenuse, or in this case . Solving for y gives the correct expression.

### Example Question #4 : Trigonometry

What is the cosine of ?

**Possible Answers:**

**Correct answer:**

The pattern for the side of a triangle is .

Since , we can plug in our given values.

Notice that the 's cancel out.

### Example Question #1 : Trigonometry

If , what is if is between and ?

**Possible Answers:**

**Correct answer:**

Recall that .

Therefore, we are looking for or .

Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of is . However, given the quadrant of our angle, it will be .