## Example Questions

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

If , where and ,

then what is ?      Explanation:

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?      Explanation:

cos = adjacent/hypotenuse = To get the radical out of the denominator, we multiply:  ### Example Question #3 : 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.      Explanation:

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 #1 : How To Find The Cosine Of An Angle

What is the of an angle with ?      Explanation:

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 #5 : How To Find The Cosine Of An Angle

Right triangle has sides  and . What is the cosine of       Explanation:

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 #6 : How To Find The Cosine Of An Angle

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