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2.3 Trigonometric Functions: The Unit Circle Approach

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

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  1. 2.3 Trigonometric Functions: The Unit Circle Approach • Definition of Trigonometric Functions • Calculator Evaluation • Application • Summary of Sign Properties

  2. Trigonometric Functions

  3. 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)

  4. 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

  5. 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

  6. Reciprocal Relationships

  7. Calculator Evaluation • Set the calculator in the proper mode for each method of evaluating trigonometric functions. Use degree mode or radian mode. • Example: Find tan 3.472 rad Solution: tan 3.472 rad ≈ .3430 • Example: Find csc 192º 47’ 22” Solution: csc 192º 47’ 22” ≈ 1/ sin 192.7894… ≈ -4.517

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