ms. battaglia ap calculus. functiondomainrange y = arcsinxy = arccosx
Post on 24-Dec-2015
225 Views
Preview:
TRANSCRIPT
5-6 Inverse Trig Functions: DifferentiationObjective: Develop properties of the 6 inverse trig functions
and differentiate an inverse trig function.
Ms. BattagliaAP Calculus
If -1 < x < 1 and –π/2 < y < π/2 then
sin(arcsinx) = x and arcsin(siny) = y
If –π/2 < y < π/2, then
tan(arctanx) = x and arctan(tany) = y
If |x| > 1 and 0 < y < π/2 or π/2 < y < π, then
Sec(arcsecx) = x and arcsec(secy) = y.
Similar properties hold for other inverse trig functions.
Properties of Inverse Trig Functions
a. Given y = arcsinx, where 0 < y < π/2, find cos y.
b. Given y = arcsec( ), find tan y.
Using Right Triangles
A photographer is taking a picture of a painting hung in an art gallery. The height of the painting is 4 ft. The camera lens is 1 ft below the lower edge of the painting. How far should the camera be from the painting to maximize the angle subtended by the camera lens?
Maximizing an Angle
top related