Pg. 385 Homework. Pg. 395 #13 – 41 odd, graph the three inverse trig functions and label the domain and range of each. Memorization quiz through inverse trig functions on Thursday!! #43 y = 3.61 sin ( x + 0.59) #44 y = -5.83 sin ( x + 2.6)
Inverse sin x
Consider y = sin x on the interval [-π/2, π/2]. Will it pass the HLT? Will it have an inverse?
An inverse can be defined as long as the domain of the original function lends itself to an inverse.
Inverse Sine Function
Inverse Cosine Functions
The inverse cosine function, denoted y = cos-1 x or y = arccosx is the function with a domain of [-1, 1] and a range of [0, π] that satisfies the relation cosy = x.
If f(x) = cosx and f-1(x) = cos-1 x(f-1 ◦ f)(x) = x on [0, π] and(f ◦ f-1)(x) = x on [-1, 1]
Inverse Tangent Function
Finding the Domain and Range
f(x) = sin-1 (2x)
g(x) = sin-1 (⅓ x)