1. WARM UP Evaluate a)2sin 2 135°– 5 tan (-45°) b)3cos 2 210°+ sin 315°

2. Section/Topic2.3a Finding Trig Functions Values Using a Calculator a)Find function values using a calculator b)Find angle measures using a calculator Objective (Trig Standard 9a) Students will be able to find trig functions values using a calculator Homework (with announcements) Page 80 (# 1 to 23 all) and get a scientific calculator Quiz on Wednesday Trig Game Plan Date: 9/30/13

3. 2 Acute Angles and Right Triangle

4. Caution When evaluating trigonometric functions of angles given in degrees, remember that the calculator must be set in degree mode.

5. Example 1 FINDING FUNCTION VALUES WITH A CALCULATOR (a) sin 49°12′ Approximate the value of each expression. ≈.75699506 (b) sec 97.977° sec 97.977° ≈ –7.205879213 Calculators do not have a secant key, so first find cos 97.977° and then take the reciprocal.

6. Example 1 FINDING FUNCTION VALUES WITH A CALCULATOR (continued) (c) Approximate the value of each expression. (d) sin (–246°) ≈.91354546 Use the reciprocal identity

7. Approximate the value of each expression. 2.3 Example 2 Finding Function Values with a Calculator (page 67)

8. 2.3 Example 2 Finding Function Values with a Calculator (cont.)

9. Angle Measures Using a Calculator Graphing calculators have three inverse functions. If x is an appropriate number, then gives the measure of an angle whose sine, cosine, or tangent is x.

10. SUMMARY GivenOn your Calculator, use:Result Angle (Degrees o ) Sin, Cos, TanDecimal (Ratio of sides) DecimalSin -1, Cos -1, Tan -1 Angle (Degrees o )

11. Example 3: Using Inverse Trigonometric Functions to Find Angles Use a calculator to find an angle in the interval that satisfies each condition. 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

12. Example 3: 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

13. Use a calculator to find an angle θ in the interval [0°, 90°] that satisfies each condition. Example 4 USING INVERSE TRIGONOMETRIC FUNCTIONS TO FIND ANGLES (a) Use degree mode and the inverse sine function. (b) Use the identity

14. Caution Note that the reciprocal is used before the inverse trigonometric function key when finding the angle, but after the trigonometric function key when finding the trigonometric function value.

15. Use a calculator to find an angle θ in the interval [0°, 90°] that satisfies each condition. Example 5a

16. Example 5b

17. Example 5c

18. Explain in at least three sentences to use a calculator to find an angle β in the interval [0°, 90°] that satisfies cot β ≈ 1.5789. Time of Duty (TOD)