# High School Math : Trigonometry

## Example Questions

### Example Question #81 : Trigonometry

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

To convert degrees to radians, set up a ratio. The ratio of degrees to radians is .

Cross multiply.

### Example Question #1811 : High School Math

How many radians are in ?

Possible Answers:

Correct answer:

Explanation:

To solve this, use a proportion. The ratio of degrees to radians is .

Cross multiply:

### Example Question #16 : Graphing The Sine And Cosine Functions

In the unit circle, what is the angle in radians that corresponds to the point (0, -1)?

Possible Answers:

Correct answer:

Explanation:

On the unit circle, (0,-1) is the point that falls between the third and fourth quadrant.  This corresponds to .

### Example Question #51 : The Unit Circle And Radians

What is the reference angle for ?

Possible Answers:

Correct answer:

Explanation:

To find the reference angle, subtract  (1 trip around the unit circle) from the given angle until you reach an angle which is less than .

### Example Question #1 : Triangles

In this figure, side , and . What is the value of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

Since , we know we are working with a right triangle.

That means that .

In this problem, that would be:

Plug in our given values:

### Example Question #1 : Triangles

Let ABC be a right triangle with sides  = 3 inches,  = 4 inches, and  = 5 inches. In degrees, what is the  where  is the angle opposite of side ?

Possible Answers:

Correct answer:

Explanation:

We are looking for . Remember the definition of  in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out  we can find

### Example Question #1 : Applying Trigonometric Functions

In this figure, if angle , side , and side , what is the measure of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

Since , we know we are working with a right triangle.

That means that .

In this problem, that would be:

Plug in our given values:

### Example Question #1 : Triangles

In this figure, , and . What is the value of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

Notice that these sides fit the pattern of a 30:60:90 right triangle: .

In this case, .

Since angle  is opposite , it must be .

### Example Question #2 : Right Triangles

A triangle has angles of . If the side opposite the angle is , what is the length of the side opposite ?

Possible Answers:

Correct answer:

Explanation:

The pattern for is that the sides will be .

If the side opposite is , then the side opposite will be .

### Example Question #1 : Applying The Law Of Cosines

In , , and . To the nearest tenth, what is  ?

Possible Answers:

A triangle with these sidelengths cannot exist.

Correct answer:

Explanation:

By the Triangle Inequality, this triangle can exist, since .

By the Law of Cosines:

Substitute the sidelengths and solve for  :