Do Now – Complete the Unit Circle

Chapter 4: Circular Functions Lesson 5: Exact Values of Sines, Cosines, and Tangents Mrs. Parziale

Example 1: Consider a rotation of 45 degrees ( or radians) -- ( Right Triangle)

Using the Unit Circle So, when, and

Example 2: Use the symmetry around the unit circle to find all points for multiples of

Consider a rotation of 30 degrees ( or radians) -- ( Right Triangle) Example 2:

Using the Unit Circle So, when, and

Example 4: Use the symmetry around the unit circle to find all points for multiples of

Consider a rotation of 60 degrees ( or radians) -- ( Right Triangle) Example 5:

Using the Unit Circle So, when, and

Example 6: Use the symmetry around the unit circle to find all points for multiples of

Example 7: CALCULATING TANGENT (x, y) = (cos , sin  ) and Let Then,

Example 8: Use the table at the start of class (All Students Take Calculus) and your knowledge of calculating tangents using sine and cosine values to calculate to following: a. b. c.

Example 9: Find the exact values of,,.

Example 10: Find the exact values of,,.

Example 11: Find the exact values of,,.

Example 12: The regular pentagon is inscribed within the unit circle. a.Give the exact coordinates of the point B. x y B A

Example 12: The regular pentagon is inscribed within the unit circle. b. Estimate the length of AB to the nearest thousandth. (hint: use the distance formula.) x y B A

Closure Identify the exact values within the first quadrant. Use the mnemonic “All Students Take Calculus” to help you identify the exact values in the second quadrant. The third quadrant? The fourth quadrant?