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6.5 – Inverse Trig Functions

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 = 2x 3 + 1?

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6.5 – Inverse Trig Functions

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  1. 6.5 – Inverse Trig Functions

  2. 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?

  3. 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?

  4. 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

  5. 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)

  6. 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)

  7. 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)

  8. Example. Evaluate tan-1(0.4) • Example. Evaluate sin-1(-1)

  9. 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

  10. Example. Evaluate arcsin(sin(3π/4)) • Do we get “x” back out?

  11. Example. Evaluate cos(arctan(0.4))

  12. Assignment • Pg. 527 • 5-33odd • 40, 41

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