### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find Positive Sine

If , what is ? Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

Recall that the sine wave is symmetrical with respect to the origin. Therefore, for any value , the value for is . Therefore, if is , then for , it will be .

### Example Question #2 : How To Find Positive Sine

In a right triangle, cos(A) = . What is sin(A)?

**Possible Answers:**

**Correct answer:**

In a right triangle, for sides a and b, with c being the hypotenuse, . Thus if cos(A) is , then c = 14, and the side adjacent to A is 11. Therefore, the side opposite of angle A is the square root of , which is Since sin is , sin(A) is .

### Example Question #3 : How To Find Positive Sine

What is the value of ?

**Possible Answers:**

**Correct answer:**

As with all trigonometry problems, begin by considering how you could rearrange the question. They often have hidden easy ways out. So begin by noticing:

Now, you can treat like it is any standard denominator. Therefore:

Combine your fractions and get:

Now, from our trig identities, we know that , so we can say:

Now, for our triangle, the is . Therefore,

### Example Question #4 : How To Find Positive Sine

Solve for :

if

**Possible Answers:**

**Correct answer:**

Recall that the standard triangle, in radians, looks like:

Since , you can tell that .

Therefore, you can say that must equal :

Solving for , you get: