# High School Math : Understanding Sine, Cosine, and Tangent

## Example Questions

### Example Question #1 : Understanding Sine, Cosine, And Tangent

If the polar coordinates of a point are , then what are its rectangular coordinates?      Explanation:

The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)

The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.  In this problem, the polar coordinates of the point are , which means that and . We can apply the conversion formulas to find the values of x and y.  The rectangular coordinates are .

The answer is .

### Example Question #1 : Trigonometry What is the ?      Explanation:  ### Example Question #3 : Understanding Sine, Cosine, And Tangent In the right triangle above, which of the following expressions gives the length of y?      Explanation: is defined as the ratio of the adjacent side to the hypotenuse, or in this case . Solving for y gives the correct expression.

### Example Question #4 : Understanding Sine, Cosine, And Tangent

What is the cosine of ?      Explanation:

The pattern for the side of a triangle is .

Since , we can plug in our given values.  Notice that the 's cancel out. ### Example Question #1 : How To Find Negative Sine

If , what is if is between and ?      Recall that .
Therefore, we are looking for or .
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of is . However, given the quadrant of our angle, it will be . 