The Inverse Cosine FunctionLesson 5.3

Reminder… y = cos x

Reminder… y = cos x

Remember… y = sin x

Remember… y = sin x

Remember… y = tan x

• Lorem

y = tan-1 x

• Lorem

To summarize Domain Range

Sin-1x -1≤ x ≤ 1 -π/2 ≤ y ≤ π/2Cos-1x -1 ≤ x ≤ 1 0 ≤ y ≤ πTan-1x Set of all reals -π/2 ≤ y ≤ π/2

Example 1• The top of the crossbar in each goal post in high

school football is 10 feet off the ground. Express the measure of the angle of elevation θ from a point halfway between the sidelines to the top of the crossbar as a function of the distance d in yards from a point directly below the middle of the crossbar.

10 feet

crossbar

Point on fieldθ

d

d

10tan )

10(tan 1

d

Example 2• If x < 0 and y > 0, write cos (sin-1(x/y)) in terms

of x and y.2nd quadrant cos is negative

x

y

θ?

x2 + ?2 = y2

?2 = y2 – x2

22? xy y

xy 22

cos

Example 3• Solve sin x = -.8245

x = arcsin(-.8245)x = -55.54˚ + 360k

2.35.5378˚ + 360kOR -.9693 + 2πk, -2.1722+2πk

Homework

Pages 4722, 14 - 17