Understanding Inverse Functions and Trigonometric Values
This homework assignment focuses on the concept of inverse functions, particularly in relation to trigonometric functions. Students will find the inverse of a given set of points and a linear function while exploring the one-to-one nature of various functions such as quadratic and cubic equations. Additionally, the assignment includes evaluating specific trigonometric values and determining exact values for inverse trigonometric functions without a calculator. It emphasizes the importance of restricted domains and ranges in transforming trigonometric functions.
Understanding Inverse Functions and Trigonometric Values
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Presentation Transcript
Warm Up • Let g(x) = {(1, 3), (2, 5), (4, 10), (-3, 7)}. What is g-1(x)? • Write the inverse of the function: f(x) = 2x – 3 • Determine whether the function is one-to-one. a) y = x2 b) y = x3 c) y = cos x • Evaluate: (a) cos (π/6) (b) cos (5π/6) (c) cos (-π/6) (d) sin(π/3) (e) sin (-π/3) (f) sin (2π/3)
Inverse Trig Functions Relate the concept of inverse functions to trig functions
Restricted Domain of sine = Range of sine = Domain of arcsin = Range of arcsin =
Inverse with the calculator… Sinx = 0.25 Sinx = 3/5 Sinx = 9/2 Sinx = -1/6 Sinx = -0.88 Cosx = 0.45 Cosx = 2/7 Cosx = -0.16 Cosx = -4/9 Cosx = 1.3
Examples: • Determine the exact value of each of the following (No Calc!) 1) arccos (-1/2) = 2) arcsin (-1/2) = 3) arccos (0) = 4) arcsin (0) = 5) arccos (-1) = 6) arcsin (-1) = 7) 8)
Complete the table using the unit circle. Rationalize all denominators.
Homework • pg 421 • #1 – 20, 23 – 31 odd, 49 and 51
