### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Secant, Cosecant, Cotangent

If and , what is the value of ?

**Possible Answers:**

**Correct answer:**

Since cotangent is positive and sine is negative, alpha must be in quadrant III. then implies that is a point on the terminal side of alpha.

### Example Question #2 : Secant, Cosecant, Cotangent

If and , then which of the following must be true about .

**Possible Answers:**

**Correct answer:**

Since cosecant is negative, theta must be in quadrant III or IV.

Since tangent is positive, it must be in quadrant I or III.

Therefore, theta must be in quadrant III.

Using a unit circle we can see that quadrant III is when theta is between and .

### Example Question #3 : Secant, Cosecant, Cotangent

The point lies on the terminal side of an angle in standard position. Find the secant of the angle.

**Possible Answers:**

**Correct answer:**

Secant is defined to be the ratio of to where is the distance from the origin.

The Pythagoreanr Triple 5, 12, 13 helps us realize that .

Since , the answer is .

### Example Question #1 : Secant, Cosecant, Cotangent

Given angles and in quadrant I, and given,

and ,

find the value of .

**Possible Answers:**

**Correct answer:**

Use the following trigonometric identity to solve this problem.

Using the Pythagorean triple 3,4,5, it is easy to find .

Using the Pythagorean triple 5,12,13, it is easy to find .

So substituting all four values into the top equation, we get

### Example Question #1 : Secant, Cosecant, Cotangent

Find the value of the trigonometric function in fraction form for triangle .

What is the secant of ?

**Possible Answers:**

**Correct answer:**

The value of the secant of an angle is the value of the hypotenuse over the adjacent.

Therefore:

### Example Question #6 : Secant, Cosecant, Cotangent

Which of the following is the equivalent to ?

**Possible Answers:**

**Correct answer:**

Since :

### Example Question #1 : Sec, Csc, Ctan

For the above triangle, what is if , and ?

**Possible Answers:**

**Correct answer:**

Secant is the reciprocal of cosine.

It's formula is:

Substituting the values from the problem we get,

### Example Question #1 : Sec, Csc, Ctan

For the above triangle, what is if , and ?

**Possible Answers:**

**Correct answer:**

Cotangent is the reciprocal of tangent.

It's formula is:

Substituting the values from the problem we get,

### Example Question #2 : Secant, Cosecant, Cotangent

Determine the value of .

**Possible Answers:**

**Correct answer:**

Rewrite in terms of sine and cosine.

### Example Question #2 : Sec, Csc, Ctan

Evaluate:

**Possible Answers:**

**Correct answer:**

Evaluate each term separately.

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