1. 14.1 The Unit Circle Part 2

2. When measuring in radians, we are finding a distance ____ the circle. This is called. What is the distance around a circle? If the circle has a radius of 1, find the circumference. around arclength Circumference

3. Converting Angle Measures

4. How many radians are in of a circle? Develop all multiples of

5. How many radians are in of a circle? Develop all multiples of

6. How many radians are in of a circle? Develop all multiples of

7. Degree and Radian equivalences: 30 º = 45 º = 60 º = 90 º = So, the coordinates for these equivalent points on the unit circle are the same for degrees and radians.

9. The Unit Circle A unit circle is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θ in the standard position:

10. Using the Unit Circle to Evaluate Trigonometric Functions Use the unit circle to find the exact value of each trigonometric function. cos 225° The angle passes through the point on the unit circle. cos 225° = x Use cos θ = x.

11. Use the unit circle to find the exact value of each trigonometric function. sin 315° sin 315° = y Use sin θ = y. The angle passes through the point on the unit circle. Using the Unit Circle to Evaluate Trigonometric Functions

12. Use the unit circle to find the exact value of each trigonometric function. The angle passes through the point on the unit circle. Using the Unit Circle to Evaluate Trigonometric Functions

13. You can use reference angles to determine the values of trigonometric functions. Trigonometric Functions and Reference Angles Step 1 Draw the angle in standard position and determine the reference angle. Step 2 Use the reference angle to input your measurements Step 3 Adjust the sign of the measurements based on the quadrant of the terminal side.

14. Using Reference Angles to Evaluate Trigonometric functions Use a reference angle to find the exact value of the sine and cosine of 330°. Step 1 Draw the angle and find the measure of the reference angle. The reference angle measures 30° Step 2 Use the reference angle to input the measurements for sine and cosine of the reference angle. Step 3 Adjust the signs, if needed.

15. Using Reference Angles to Evaluate Trigonometric functions Use a reference angle to find the exact value of the sine and cosine of 270°. Step 1 Draw the angle and find the measure of the reference angle. The reference angle measures 90° Step 2 Use the reference angle to input the measurements for sine and cosine of the reference angle. Step 3 Adjust the signs, if needed. 270° sin 270° = – 1 cos 270° = 0

16. Using Reference Angles to Evaluate Trigonometric functions Use a reference angle to find the exact value of the sine and cosine of Step 1 Draw the angle and find the measure of the reference angle. Step 2 Use the reference angle to input the measurements for sine and cosine of the reference angle. Step 3 Adjust the signs, if needed. The reference angle measures

17. Using Reference Angles to Evaluate Trigonometric functions Use a reference angle to find the exact value of the sine and cosine of -30°. Step 1 Draw the angle and find the measure of the reference angle. The reference angle measures 30° Step 2 Use the reference angle to input the measurements for sine and cosine of the reference angle. Step 3 Adjust the signs, if needed. – 30°