# Precalculus : Graphing the Sine and Cosine Functions

## Example Questions

### Example Question #11 : Graphs And Inverses Of Trigonometric Functions

A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?

Explanation:

We can apply the Law of Cosines to find the measure of this angle, which we will call :

The widest angle will be opposite the side of length 22, so we will set:

### Example Question #12 : Graphs And Inverses Of Trigonometric Functions

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

A triangle with these characteristics cannot exist.

Explanation:

By the Law of Cosines:

or, equivalently,

Substitute:

### Example Question #13 : Graphs And Inverses Of Trigonometric Functions

What is the period of

?

Explanation:

The period for  is . However, if a number is multiplied by , you divide the period  by what is being multiplied by . Here,  is being multiplied by    equals

### Example Question #1 : Understanding Trigonometric Functions

Which of the following is not in the range of the function ?

Explanation:

The range of the function  is all numbers between  and  (the sine wave never goes above or below this).

Of the choices given,  is greater than  and thus not in this range.

### Example Question #15 : Graphs And Inverses Of Trigonometric Functions

What is the  of ?

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

### Example Question #16 : Graphs And Inverses Of Trigonometric Functions

What is the  of ?

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

### Example Question #1831 : High School Math

In a right triangle, if

and

then what does  equal?

Explanation:

One can draw a right triangle with acute angles  and . The side adjacent to  is 4, and the side adjacent to   is 3.

### Example Question #18 : Graphs And Inverses Of Trigonometric Functions

Bob manages a pizza store. He bought a new machine that tracks how big his employees are cutting the pizza slices. The machine measures the average angle size of each slice of each pizza. Unfortunately, the angle is given as 0.7854 radians which Bob does not understand. Help Bob by converting the radian angle into degrees. In degrees, what is the size of the angle for an average pizza slice.

Explanation:

To convert we use a common conversion amount. It may be easiest to remember the full circle example. In degrees, a full circle is  around. In terms of radians, a full circle is . So to get our answer

### Example Question #19 : Graphs And Inverses Of Trigonometric Functions

Explanation:

To convert from degrees to radians, one multiplies by .

### Example Question #20 : Graphs And Inverses Of Trigonometric Functions

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