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Trig./Pre-Calc 4.7A Inverse Trig. Functions Inverse Sine: Definition of the Inverse Trigonometric Functions: Function Domain Range y = arcsin x if and only if sin y = x 1 x 1 y = arcos x if and only if cos y = x 1 x 1 0 y y = arctan x if and only if tan y = x x Inverse Properties If 1 x 1 and 2 y 2 , then sin(arcsin x) = x and arcsin(sin y) = y. If 1 x 1 and 0 y , then cos(arcos x) = x and arcos(cos y) = y. If 2 y 2 , then tan(arctan x) = x and arctan(tan y) = y. 2 2 y y 2 2 Example #1 Evaluate the given expression without the aid of a calculator. 1 2 a) arcsin c) arctan( 3 ) b) arctan 3 3 d) arcsin 3 2 Example #2 Use a calculator to approximate the value. (Round your answers to two decimal places.) a) cos 1 0.75 b) arctan 6 c) arccos 0.51 Example #3 Use the properties of inverse trigonometric functions to evaluate the expression. a) sin arcsin 0.7 b) cosarccos 0.3 c) arcsin sin 3 Example #4 Find the exact value of the expression without using a calculator. (Hint: make a sketch of a right triangle.) a) sin(arctan 34 ) b) cos(arcsin 5 13 ) Example #5 Write an algebraic expression that is equivalent to the expression. (Hint: sketch a right triangle.) a) cot(arctan x) b) sin(arccos x) c) x csc arctan 2 4.7A HW: Pg. 327 #2-8 even, 16-24 even, 30-40 even, 48-58 even, 106