Trigonometric Functions and Calculator Applications

Explore how calculators can be used to find trigonometric function values, approximate expressions, and determine angles using inverse trigonometric functions. Learn about evaluating functions in degree mode and utilizing reciprocal identities for accurate calculations.

• Trigonometry
• Calculator Applications
• Inverse Functions
• Angle Measures
• Reciprocal Identities

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1. Warm Up Find the values of the six trigonometric functions for 300

2. Section 2.3 Finding Trigonometric Function Values Using a Calculator Objective: SWBAT find trig function values using a calculator.

3. Function Values Using a Calculator Calculators are capable of finding trigonometric function values. When evaluating trigonometric functions of angles given in degrees, remember that the calculator must be set in degree mode. Remember that most calculator values of trigonometric functions are approximations.

4. Finding Function Values with a Calculator Approximate the value of each expression. sin38 24 b) cot 68.4832 Use the identity a) 24 6 0 1 = = 38 24 38 38.4 = cot . tan = sin38 24 si .6211477 n 38.4 cot 68.4832 .3942492

5. FINDING FUNCTION VALUES WITH A CALCULATOR Approximate the value of each expression. (a) sin 49 12 .75699506 (b) sec 97.977 Calculators do not have a secant key, so first find cos 97.977 and then take the reciprocal. sec 97.977 .75699506

6. FINDING FUNCTION VALUES WITH A CALCULATOR Approximate the value of each expression. (c) Use the reciprocal identity (d) sin ( 246 ) .91354546

7. Angle Measures Using a Calculator REMEMBER: Graphing calculators have three inverse functions. 1 sin ,cos x -1 1 or tan x , x If x is an appropriate number, then gives the measure of an angle whose sine, cosine, or tangent is x.

8. Using Inverse Trigonometric Functions to Find Angles Use a calculator to find an angle in the interval that satisfies each condition. [0 ,90 ] sin .8535508 Using the degree mode and the inverse sine function, we find that an angle having sine value .8535508 is 58.6 . We write the result as 1 sin .8535508 58.6

9. Using Inverse Trigonometric Functions to Find Angles continued Use the identity Find the reciprocal of 2.48679 to get Now find using the inverse cosine function. The result is 66.289824 sec 2.486879 1 = cos . sec cos .4021104.

10. USING INVERSE TRIGONOMETRIC FUNCTIONS TO FIND ANGLES Use a calculator to find an angle in the interval [0 , 90 ] that satisfies each condition. (a) Use degree mode and the inverse sine function. (b) Use the identity

11. Homework Page 64 # 5-28 evens