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Lesson 5-5 [Book: 15-25 ALL, 28-31 ALL, 36-39 ALL, 45a, 46, 52-54 ALL, 58-60 ALL] Objectives 1. 2. 3. If you look at the chart on page 305, you will see that when we take the sine, cosine, or tangent of a(n) ____________, we get a(n) _____________. Today, we will talk about what we have to do if we already know a(n) ______________, and we have to find a(n) __________________. Let’s demonstrate using a 30-60-90 triangle. So, if we already know the trigonometric ratio, we must use the __________________ of the trigonometric function in order to find the unknown angle. INVERSE TRIGONOMETRIC FUNCTIONS + + + *Check the table on page 306 Ex. 1 Solve each equation. b) sin x = a) tan x = 1 1 2 Ex. 2 Evaluate each expression. Assume all angles are in Quadrant I. a) tan (tan -1 6 ) 11 b) tan (arccos 4 ) 5 We can also use the inverse trig functions on our calculator to find missing parts of a right triangle. If we are using the inverse sine, cosine, or tangent, what part of a triangle are we trying to find? Ex. 3 If g = 28 and h = 21, find H. Ex. 4 If a 100-foot building casts an 88-foot shadow. What is the angle of elevation of the sun? Solve a triangle - Ex. 5 Solve Triangle JKL when given the following descriptions. a) K = 40 k = 26 b) j = 65 55 Name ________________________________ Date _____________ Quiz – 5-1 through 5-4 Advanced Math Directions: You have 10 minutes to take this quiz. You may NOT use any resource other than your own brain. 1. How many seconds are in a degree? 2. If we draw an angle by making 2 full counterclockwise rotations, then how many degrees is that angle? 3. Find one angle that is coterminal to 60 degrees. 4. Draw a unit circle or a reference triangle and find sec 30 . 5. If A = 38 and a = 14, find c to the nearest tenth.