# ACT Math : How to find negative sine

## Example Questions

### Example Question #5 : Understanding Sine, Cosine, And Tangent

If , what is  if  is between  and ?

Explanation:

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 .

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

What is the sine of the angle formed between the origin and the point  if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ?

Explanation:

You can begin by imagining a little triangle in the fourth quadrant to find your reference angle.  It would look like this:

Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, , where  and  are leg lengths and  is the length of the hypotenuse, the hypotenuse is , or, for our data:

The sine of an angle is:

For our data, this is:

Since this is in the fourth quadrant, it is negative, because sine is negative in that quadrant.

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

What is the sine of the angle formed between the origin and the point  if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ?

Explanation:

You can begin by imagining a little triangle in the third quadrant to find your reference angle. It would look like this:

Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, , where  and  are leg lengths and  is the length of the hypotenuse, the hypotenuse is , or, for our data:

The sine of an angle is:

For our data, this is:

Since this is in the third quadrant, it is negative, because sine is negative in that quadrant.

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

If , what is the value of  if ?