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6.5 – Inverse Trig Functions Review/Warm Up • 1) Can you think of an angle ϴ, in radians, such that sin(ϴ) = 1? • 2) Can you think of an angle ϴ, in radians, such that cos(ϴ) = -√3/2 • 3) From precalculus, do you remember how to solve for the inverse function if y = 2x3 + 1? • 4) How can you verify whether two functions are inverses of one another? Use the inverse you found for the function above. • 5) Say you know all three sides from a right triangle. Can you think of a way to determine the other missing degree angles? • Like other functions from precalculus, we may also define the inverse functions for trig functions • In the case of trig function, why would the inverse be useful? • Say you know sin(ϴ) = 0.35 – Do we know an angle ϴ off the top of our heads that would give us this value? • The inverse is there for us to now determine unknown angles The Inverse Functions • There are two ways to denote the inverse of the functions • If y = sin(x), x = arcsin(y) • OR • If y = sin(x), x = sin-1(y) • • • • Similar applies to the others If y = cos(x), x = arccos(y) OR If y = cos(x), x = cos-1(y) • If y = tan(x), x = arctan(y) • OR • If y = tan(x), x = tan-1(x) Finding the inverse • To find the inverse, or ϴ of each function, we generally will use our graphing calculator to help us • Example. Evaluate arccos(0.3) • Example. Evaluate tan-1(0.4) • Example. Evaluate sin-1(-1) • In the case of inverse trig functions, f-1(f(x)) and f(f-1(x)) is not necessarily = x • Always evaluate trig functions as if using order of operations; inside of parenthesis first • Example. Evaluate arcsin(sin(3π/4)) – Do we get “x” back out? • Example. Evaluate cos(arctan(0.4)) • • • • Assignment Pg. 527 5-33odd 40, 41