### All Trigonometry Resources

## Example Questions

### Example Question #1 : Angles In The Unit Circle

What are the ways to write 360^{o} and 720^{o} in radians?

**Possible Answers:**

**Correct answer:**

on the unit circle.

on the unit circle.

### Example Question #1 : Angles In The Unit Circle

Which of the following is not an angle in the unit circle?

**Possible Answers:**

**Correct answer:**

The unit circle is in two increments: : , etc. and : , etc. The only answer choice that is not a multiple of either or is .

### Example Question #1 : Angles In The Unit Circle

What is the equivalent of , in radians?

**Possible Answers:**

**Correct answer:**

To convert from degrees to radians, use the equality

or .

From here we use as a unit multiplier to convert our degrees into radians.

### Example Question #4 : Angles In The Unit Circle

What is the value of ?

**Possible Answers:**

**Correct answer:**

To help with this one, draw a 45-45-90 triangle. With legs equal to 1 and a hypotenuse of .

Then, use the definition of tangent as opposite over adjacent to find the value.

Since the legs are congruent, we get that the ratio is 1.

### Example Question #5 : Angles In The Unit Circle

What is ?

**Possible Answers:**

**Correct answer:**

Recall that on the unit circle, sine represents the y coordinate of the unit circle.

Then, since we are at 90˚, we are at the positive y axis, the point (0,1).

At this point on the unit circle, the y value is 1.

Thus .

### Example Question #6 : Angles In The Unit Circle

Which of the following is NOT a special angle on the unit circle?

**Possible Answers:**

**Correct answer:**

For an angle to be considered a special angle, the angle must be able to produce a or a triangle.

The only angle that is not capable of the special angles formation is .

### Example Question #7 : Angles In The Unit Circle

For which values of , where in the unit circle, is undefined?

**Possible Answers:**

**Correct answer:**

Recall that . Since the ratio of any two real numbers is undefined when the denominator is equal to , must be undefined for those values of where . Restricting our attention to those values of between and , when or . Hence, is undefined when or .

### Example Question #8 : Angles In The Unit Circle

If and , then =

**Possible Answers:**

The solution does not lie in the given interval.

**Correct answer:**

We first make the substitution .

In the interval , the equation has the solution .

Solving for ,

.

### Example Question #9 : Angles In The Unit Circle

What is the value of from the unit circle?

**Possible Answers:**

**Correct answer:**

From the unit circle, the value of

.

This can be found using the coordinate pair associated with the angle which is .

Recall that the pair are .

### Example Question #10 : Angles In The Unit Circle

What is

,

using the unit circle?

**Possible Answers:**

**Correct answer:**

Recall that the unit circle can be broken down into four quadrants. Each quadrant has similar coordinate pairs basic on the angle. The only difference between the actual coordinate pairs is the sign on them. In quadrant I all signs are positive. In quadrant II only sine and cosecant are positive. In quadrant III tangent and cotangent are positive and quadrant IV only cosine and secant are positive.

has the reference angle of and lies in quadrant IV therefore .

From the unit circle, the coordinate point of

corresponds with the angle .