1. Trigonometric Functions: The Unit Circle
Objectives:
Identify a unit circle
Evaluate trigonometric functions using the unit circle and a calculator

2. The Unit Circle

3. The Unit Circle
As the real number line wraps around the unit circle, each real number corresponds to a point on the circle. For example, the real number corresponds to the point
In general, each real number corresponds to a central angle (in standard position) whose radian measure is
It follows that the coordinates are two functions of the real variable .

4. Definitions of Trigonometric functions
Let be a real number and let be the point on the unit circle corresponding to .

5. EX: Evaluate the six trigonometric functions at each real number1. 2.

6. EX: Evaluate the six trigonometric functions at each real number3. 4.

7. EX: Evaluate the six trigonometric functions at each real number5. 6.

8. EX: Evaluate the six trigonometric functions at each real number7. 8.

9. Evaluating trigonometric function
When evaluating a trigonometric function with a calculator, you need to set the calculator to the desired mode of measurement (degree or radian). Most calculators do not have keys for cosecant, secant, and cotangent functions. To evaluate these functions, you can use the reciprocal key with their respective reciprocal functions: sine, cosine and tangent. Round the answers to four decimal places.

10. EX: Use a calculator to evaluate the trigonometric function.
Degrees
Radians 9.
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