1. C HAPTER 14 D AY 6 Inverse Trigonometric Functions

2. 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 2 π in radians and between 0° and 360° in degrees.

3. F IND SUCH THAT. 1. Is positive or negative? In which quadrant(s) is the sin value positive? What real number,, has a y-coordinate of ?

4. F IND 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 ?

5. F IND 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?

6. F IND 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 ?

7. F IND SUCH THAT. 5.6.

8. F IND SUCH THAT. 7.8.

9. F IND SUCH THAT. 9.10.

10. F IND SUCH THAT. 11.12.

11. 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. 360 º 2π2π

12. F IND ALL VALUES OF FOR WHICH THE TERMINAL SIDE OF IN STANDARD POSITION PASSES THROUGH THE GIVEN POINT. G IVE YOUR ANSWER IN DEGREES AND RADIANS. 13.

13. F IND ALL VALUES OF FOR WHICH THE TERMINAL SIDE OF IN STANDARD POSITION PASSES THROUGH THE GIVEN POINT. G IVE YOUR ANSWER IN DEGREES AND RADIANS. 14.