2.3 Trigonometric Functions: The Unit Circle Approach

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2.3 Trigonometric Functions: The Unit Circle Approach. Definition of Trigonometric Functions Calculator Evaluation Application Summary of Sign Properties. Trigonometric Functions. The Unit Circle .

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2.3 Trigonometric Functions: The Unit Circle Approach
• Definition of Trigonometric Functions
• Calculator Evaluation
• Application
• Summary of Sign Properties
The Unit Circle

If a point (a,b) lies on the unit circle, then the following are true for the angle x associated with that point:

sin x = b

cos x = a

tan x = b/a (a ≠ 0)

csc x = 1/b (b ≠ 0)

sec x = 1/a (a ≠ 0)

cot x = a/b (b ≠ 0)

Evaluating Trigonometric Functions

Example:

Find the exact values of the 6 trigonometric functions for the point (-4, -3)

The Pythagorean Theorem shows that the distance from the point to the origin is 5.

sin x = -3/5

cos x = -4/5

tan x = 3/4

csc x = -5/3

sec x = -5/4

cot x = 4/3

Using Given Information to Evaluate Trigonometric Functions
• Example:
• Given that the terminal side of an angle is in Quadrant IV and cos x = 3/5 find the remaining trigonometric functions.
• b2 = 25 – 9 = 16, so b = 4
• Sin x = 4/5, tan x = -4/3, csc x = -5/4,
• sec x = 5/3 and cot x = -3/4
Calculator Evaluation
• Set the calculator in the proper mode for each method of evaluating trigonometric functions. Use degree mode or radian mode.
• Example: