### All ACT Math Resources

## Example Questions

### Example Question #30 : Cosine

If , where and ,

then what is ?

**Possible Answers:**

**Correct answer:**

In the triangle below, the tangent of , or the opposite side of the angle divided by the adjacent side of the angle. According to the Pythagorean

Theorem, the

Thus the hypotenuse equals .

The cosine of an angle is the adjacent side of the angle divided by the hypotenuse of the triangle, giving us .

However, since is , and when is between , is positive while is negative. Thus, is negative, giving us the final answer of .

### Example Question #1 : How To Find The Cosine Of An Angle

What is cos θ?

**Possible Answers:**

**Correct answer:**

cos = adjacent/hypotenuse =

To get the radical out of the denominator, we multiply:

### Example Question #2 : How To Find The Cosine Of An Angle

What is the cosine of the angle formed between the -axis and the line passing through with a slope of ? Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

You do not even need to compute the line for this question. All that you need to do is note that you can make a little right triangle with a height of and a base of , which you get from the slope of the line. So, to compute the cosine, you will need to find the hypotenuse using the Pythagorean theorem:

So, our little triangle looks like:

The cosine will be the adjacent side, , divided by the hypotenuse, :

, or approximately .

### Example Question #3 : How To Find The Cosine Of An Angle

What is the of an angle with ?

**Possible Answers:**

**Correct answer:**

Since the sine of the angle is , that means the opposite side of the triangle is and the hypotenuse is . Automatically, you know this is a special 3-4-5 right triangle, and that the missing side is 3. If not, you could also find the 3rd side by doing Pythagorean Theorem. This gives you your answer of

### Example Question #4 : How To Find The Cosine Of An Angle

Right triangle has sides , and . What is the cosine of ?

**Possible Answers:**

**Correct answer:**

**SOHCAHTOA **tells us that , and we know the hypotenuse is the longest side of the triangle, . Our adjacent side will be the other side that has as a vertex, .

Thus, .

### Example Question #5 : How To Find The Cosine Of An Angle

Right triangle has sides , and . What is the cosine of ?

**Possible Answers:**

**Correct answer:**

**SOHCAHTOA **tells us that , and we know the hypotenuse is the longest side of the triangle, . Our adjacent side will be the other side that has as a vertex, .

Thus, .

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