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AA 13-7 Inverse Trig Functions Inverse: * When we flip the x and y coordinates. CAPITAL letters will be used to distinguish Trig. Functions with restricted domains from the usual functions. y = Sin x iff y = sin x and -π ≤ x ≤ π 2 2 EX: y = sin x has the inverse x = sin y Principal Values: * When we restrict the domain of a trig. function so that the inverse is a function. * The values of our restricted domains. Inverse of the Sine function: * called the Arcsine function * Symbols: sin -1 or Arcsin * Domain is set of real numbers from -1 to 1 * Range is the set of angle measures from -π ≤ x ≤ π 2 2 * read as "the angle whose sine is x" * means you are looking for the angle measure. Arccosine and Arctangent have similar properties. y = Cos x iff y = cos x and 0≤x≤π y = Tan x iff y = tan x and -π ≤ x ≤ π 2 2 Inverse Sine, Cosine, and Tangent: * Given y = Sin x, the inverse Sine function is defined by y = sin-1x or y = Arcsin x. * Given y = Cos x, the inverse Cosine function is defined by y = cos-1x or y = Arccos x. * Given y = Tan x, the inverse Tangent function is defined by y = tan-1x or y = Arctan x. 1. Solve Sin x = √2 by finding the value of 2 x to the nearest degree. 3. DRAWBRIDGE. Each leaf of a double-leaf drawbridge is 130 feet long. If a 100-foot wide ship needs to pass through the bridge, what is the minimum angle , to the nearest degee, which each leaf of the bridge should open so that the ship will fit? 2. Write each equation in the form of an inverse function. a. Tan = x b. cos α = 0.5 4. Find the each value. Write angle measures in radians. Round to the nearest hundredth. a. Arcsin √2 2 b. tan (Cos -1 4 ) 5 13 - 7 Inverse Trigonometric Functions DAY 1: pg. 749 - 751 # 15, 16, 20, 21 - 23, 27 - 32, 39 - 41, 45, 53, 58, 60, 61 (20 problems) Day 2: pg. 749 - 751 #17 - 19, 24 - 26, 33 - 38, 42 - 44, 46, 54, 59, 62 (19 problems)