CHAPTER 14 DAY 6Inverse Trigonometric

Functions

Sometimes you will be given the value of the trigonometric function and you will need to work backwards to find the point on the unit circle that corresponds to that value.

Typically you will be looking at one revolution of the unit circle – so between 0 and 2π in radians and between 0° and 360° in degrees.

FIND SUCH THAT .

1.

Is positive or negative?

In which quadrant(s) is the sin value positive?

What real number, , has a y-coordinate of ?

0 2

sin 32

32

32

FIND SUCH THAT .

2.

Is positive or negative?

In which quadrant(s) is the cos value negative?

What is the reciprocal of ?

What real number, , has a x-coordinate of ?

0 2

sec 2

2

2

22

FIND SUCH THAT .

3.

positive or negative?

Where on the unit circle is tangent undefined?

What values on the unit circle have an x-coordinate of 0?

0o 360o

tan no solution

FIND SUCH THAT .

4.

positive or negative?

In which quadrant(s) is the csc value positive?

What is the reciprocal of 2?

What real number, , has a y-coordinate of ?

0o 360o

csc 2

12

FIND SUCH THAT .

5. 6.

0 2

cot 3 cos 12

FIND SUCH THAT .

7. 8.

0 2

csc no solution cos 22

FIND SUCH THAT .

9. 10.

0o 360o

sin 32

cos 32

FIND SUCH THAT .

11. 12.

0o 360o

sin 0 tan 1

We can also find all values by adding in a full circle times a constant, k, which represent the number of revolutions around the unit circle. In degrees this would be and in radians this would be .

When given an ordered pair, we can use x, y, and r to find one trig function. Since we know what quadrant the point is located in, we are able to find the angle .

360º2π

FIND ALL VALUES OF FOR WHICH THE TERMINAL SIDE OF IN STANDARD POSITION PASSES THROUGH THE GIVEN POINT. GIVE YOUR ANSWER IN DEGREES AND RADIANS.

13.

2 3, 2

FIND ALL VALUES OF FOR WHICH THE TERMINAL SIDE OF IN STANDARD POSITION PASSES THROUGH THE GIVEN POINT. GIVE YOUR ANSWER IN DEGREES AND RADIANS.

14.

9,9