# SAT II Math I : Secant, Cosecant, Cotangent

## Example Questions

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

If  and , what is the value of ?

Explanation:

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 #1 : Secant, Cosecant, Cotangent

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

Explanation:

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 #1 : Secant, Cosecant, Cotangent

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

Explanation:

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 .

Explanation:

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 #2 : Secant, Cosecant, Cotangent

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

What is the secant of ?

Explanation:

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

Therefore:

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

Which of the following is the equivalent to ?

Explanation:

Since :

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

For the above triangle, what is  if  and ?

Explanation:

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 ?

Explanation:

Cotangent is the reciprocal of tangent.

It's formula is:

Substituting the values from the problem we get,

### Example Question #21 : Trigonometry

Determine the value of .

Explanation:

Rewrite  in terms of sine and cosine.

Evaluate: