# High School Math : Trigonometry

## Example Questions

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### Example Question #1 : Understanding Sine, Cosine, And Tangent

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

Explanation:

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 .

What is the ?

Explanation:

### Example Question #1 : Understanding Sine, Cosine, And Tangent

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

Explanation:

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 : Understanding Sine, Cosine, And Tangent

What is the cosine of ?

Explanation:

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 #5 : Understanding Sine, Cosine, And Tangent

If , what is  if  is between  and ?

Explanation:

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 .

### Example Question #1 : Trigonometry

An angle has a cosine of . What will its cosecant be?

Explanation:

The problem tells us that the cosine of the angle will be . Cosine is the adjacent over the hypotenuse. From here we can use the Pythaogrean theorem:

Now we know our opposite, adjacent, and hypotenuse.

The cosecant is .

From here we can plug in our given values.

### Example Question #1 : Trigonometry

Which of these is equal to  for angle ?

Explanation:

, as it is the inverse of the  function.  This is therefore the answer.

### Example Question #1 : Trigonometry

What is  if  and ?

Explanation:

In order to find  we need to utilize the given information in the problem.  We are given the opposite and adjacent sides.  We can then, by definition, find the  of  and its measure in degrees by utilizing the  function.

Now to find the measure of the angle using the  function.

If you calculated the angle's measure to be  then your calculator was set to radians and needs to be set on degrees.

### Example Question #3 : Trigonometry

What is ?

Explanation:

To get rid of , we take the or of both sides.