### 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 .

### Example Question #1 : Trigonometry

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

**Possible Answers:**

**Correct answer:**

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 : Trigonometric Operations

Which of these is equal to for angle ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Arcsin, Arccos, Arctan

What is if and ?

**Possible Answers:**

**Correct answer:**

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 #1 : Trigonometry

What is ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Trigonometry

**Possible Answers:**

**Correct answer:**

In order to find we need to utilize the given information in the problem. We are given the opposite and hypotenuse 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.