Inverse Trig Functions. If cos (x) = 0 then what is x?

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Presentation transcript:

Inverse Trig Functions

If cos (x) = 0 then what is x?

cos /2 = 0 cos 3 /2 = 0 Answer: every odd or (2n+1) where n=0,1,2,3… (1,0)(-1,0) (0,-1)

In Algebra you learned to switch x & y to find the inverse function If y = cos x Then x = cos y …solving for y, we write…

y = cos -1 (x) is not a function WHY? Fails the horizontal line test There is more than one value of x for each value of y Examples: cos -1 ( 90 o) = 0 cos -1 ( 270 o) = 0

HOW CAN we restrict the domain of y=cos x so that cos -1 x is a function?

0 to ……. Range of y=cos -1 (x) will be restricted too.

cos(x) restricted Domain: Range:

y=cos(x) and y=cos -1 (x) are reflections over y = x Click here to look…

y = cos -1 (x) List the… DOMAIN: RANGE:

y = sin x fails the horizontal line test Let’s restrict it!

y = sin x restricted Domain Range

REFLECT y = sin x over y = x to graph y = sin -1 x Switch x and y and plot the 3 points…

y = sin -1 (x)? Domain: Range:

RELATE & EXTEND: graph y = tan -1 x Graph y = tan x Restrict the domain Reflect over y = x State DOMAIN and RANGE of y = tan -1 x

Evaluate: cos -1 = x Where between 0 and is cos(x) = Use chart of trig values to help!!!

Chart Sin x0½1 Cos x1½0

cos -1 = x The angle between 0 and is 45 degrees or Since the ratio is negative the angle must be between and

Evaluate

Chart Sin x0½1 Cos x1½0

What is ?

Chart sin x0½1 cos x1½0

SNOWBALL FIGHT! 1. YOUR NAME on one side 2. Problem on back 3. Answer on separate sheet 4. #1-3, leaving space on answer sheet NO CALCULATORS!