Chapter 9 Trigonometric Functions Section 1 Trigonometric Functions Review (Part 1)

2 Barnett/Ziegler/Byleen Business Calculus 12e Learning Objectives for Section 9.1 Trigonometric Review The student will be able to ■ Express angles in degree and radian measure ■ Work with trigonometric functions

3 Prerequisite Skills  Identify the lengths of the sides (in terms of x) of each special right triangle shown below: Barnett/Ziegler/Byleen Business Calculus 12e

4 Prerequisite Skills  Find the lengths of the each side of each special right triangle shown below: Barnett/Ziegler/Byleen Business Calculus 12e

5 Degrees and Radians Angles are measured in degrees, where there are 360º in a circle. Angles are also measured in radians, where there are 2  radians in a circle. Degree-Radian Conversion Formula

6 Barnett/Ziegler/Byleen Business Calculus 12e Degrees and Radians (continued)

7 Barnett/Ziegler/Byleen Business Calculus 12e Trigonometric Functions Consider a unit circle with center at the origin. Let point P be on the circle such that the ray from the origin through P forms an angle of  with the positive x axis. P (x, y)  (1, 0) (0, 1) (-1, 0) (0, -1)

8 Barnett/Ziegler/Byleen Business Calculus 12e Trigonometric Functions P (x, y) (1, 0)  (0, 1) x y 1 The cosine of the angle is the x-coordinate and the sine is the y-coordinate of the point P.

9 Barnett/Ziegler/Byleen Business Calculus 12e Sine and Cosine of Special Angles 1.Fill out blank unit circle with common degree and radian angles. 2.Then fill in their exact cosine and sine values. 3.Note: On the quizzes & test, you will only be given the first quadrant of the unit circle.

10 Evaluating Trig Functions Barnett/Ziegler/Byleen Business Calculus 12e

11 Evaluating Trig Functions Barnett/Ziegler/Byleen Business Calculus 12e

12 Barnett/Ziegler/Byleen Business Calculus 12e Other Trig Functions The four other trigonometric functions are

13 Evaluating Other Trig Functions  Use your unit circle to find the exact value of: Barnett/Ziegler/Byleen Business Calculus 12e

14 Trig Identities  From the unit circle and the Pythagorean Theorem, we can derive the most basic trig identity: Barnett/Ziegler/Byleen Business Calculus 12e  (1, 0) (0, 1) P (x, y)

15 Application Barnett/Ziegler/Byleen Business Calculus 12e

16 Barnett/Ziegler/Byleen Business Calculus 12e On Feb. 1, there are $1 million in revenue for 1 month of sales. 2 months after Feb. 1, there are $2.5 million in revenue for 1 month of sales. 3 months after Feb. 1, there are $4 million in revenue for 1 month of sales.

17 Homework Barnett/Ziegler/Byleen Business Calculus 12e