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

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

2 Acute Angles and Right Triangle

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

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

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

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

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

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.

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

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 is We write the result as

Example 3: Using Inverse Trigonometric Functions to Find Angles continued Use the identity Find the reciprocal of to get Now find using the inverse cosine function. The result is

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

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.

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

Example 5b

Example 5c

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