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Warm Up Convert each measure from degrees to radians. 1. 120° 2. 180°

Warm Up Convert each measure from degrees to radians. 1. 120° 2. 180° Find the exact value of each trigonometric function. 3. 4. Learning Goals. 13.4.1 Evaluate inverse trigonometric functions. 13.4.4 Use trigonometric equations & inverse trigonometric functions to solve problems.

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Warm Up Convert each measure from degrees to radians. 1. 120° 2. 180°

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  1. Warm Up Convert each measure from degrees to radians. 1. 120° 2. 180° Find the exact value of each trigonometric function. 3. 4. Learning Goals 13.4.1 Evaluate inverse trigonometric functions. 13.4.4 Use trigonometric equations & inverse trigonometric functions to solve problems. The expression sin-1 is read as “the inverse sine.” In this notation,-1 indicates the inverse of the sine function, NOT the sine function to the ______ ____________. Example 1: Finding Trigonometric Inverses Find all possible _________________ values. A. cos-1 B. tan-1 1 • sin-1(-½).

  2. Notice that more than one θhas the same output for any trig function. EXAMPLE: So, we have to restrict the domain for the function so we can find _________ angle instead of __________________ angles to correspond with the value. Trigonometric functions with restricted domains are indicated __________ ___ _____________ _____________. • How many values does tan-1 1 have? • How many values does Tan-11 have? • How what sort of values do you plug in to Sin, Cos, and Tan? • What sort of values do you plug in to Sin-1, Cos-1, and Tan-1?

  3. Example 2: Evaluating Inverse Trigonometric Functions Evaluate each inverse trigonometric function. Give your answer in both radians and degrees. A B. C. D. E. Sin-1 F. Tan-1 (0)

  4. Solve each equation to the nearest tenth. Use the given restrictions. A. sin θ = 0.4, for – 90° ≤ θ ≤ 90° B. sin θ = 0.4, for 90° ≤ θ ≤ 270° C. tan θ = –2, for –90° < θ < 90° D. tan θ = –2, for 90° < θ < 180°

  5. Example 3: Solving Trigonometric Equations Solve each equation to the nearest tenth. Use the given restrictions. C. cos θ = 0.3, for 0° ≤ θ ≤ 180° D. cos θ = 0.3, for 270° < θ < 360° Example 4: Safety Application A. A painter needs to lean a 30 ft ladder against a wall. Safety guidelines recommend that the distance between the base of the ladder and the wall should be ¼ of the length of the ladder. To the nearest degree, what acute angle should the ladder make with the ground? B. A group of hikers wants to walk form a lake to an unusual rock formation. The formation is 1 mile east and 0.75 mile north of the lake. To the nearest degree, in what direction should the hikers head from the lake to reach the rock formation?

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