Download y = sin x has the inverse x = sin y Principal Values

AA
13-7 Inverse Trig Functions
Inverse:
* When we flip the x and y coordinates.
CAPITAL letters will be used to distinguish
Trig. Functions with restricted domains from
the usual functions.
y = Sin x iff y = sin x and
-π ≤ x ≤ π
2
2
EX: y = sin x has the inverse x = sin y
Principal Values:
* When we restrict the domain of a trig.
function so that the inverse is a function.
* The values of our restricted domains.
Inverse of the Sine function:
* called the Arcsine function
* Symbols: sin -1 or Arcsin
* Domain is set of real numbers from -1 to 1
* Range is the set of angle measures from
-π ≤ x ≤ π
2
2
* read as "the angle whose sine is x"
* means you are looking for the angle
measure.
Arccosine and Arctangent have similar
properties.
y = Cos x iff y = cos x and
0≤x≤π
y = Tan x iff y = tan x and
-π ≤ x ≤ π
2
2
Inverse Sine, Cosine, and Tangent:
* Given y = Sin x, the inverse Sine function
is defined by y = sin-1x or y = Arcsin x.
* Given y = Cos x, the inverse Cosine
function is defined by y = cos-1x or
y = Arccos x.
* Given y = Tan x, the inverse Tangent
function is defined by y = tan-1x or
y = Arctan x.
1. Solve Sin x =
√2
by finding the value of
2
x to the nearest degree.
3.
DRAWBRIDGE. Each leaf of a double-leaf drawbridge is
130 feet long. If a 100-foot wide ship needs to pass through
the bridge, what is the minimum angle , to the nearest
degee, which each leaf of the bridge should open so that
the ship will fit?
2. Write each equation in the form of an
inverse function.
a. Tan = x
b. cos α = 0.5
4. Find the each value. Write angle
measures in radians. Round to the
nearest hundredth.
a. Arcsin √2
2
b. tan (Cos
-1 4
)
5
13 - 7 Inverse Trigonometric Functions
DAY 1:
pg. 749 - 751
# 15, 16, 20, 21 - 23, 27 - 32, 39 - 41,
45, 53, 58, 60, 61 (20 problems)
Day 2:
pg. 749 - 751
#17 - 19, 24 - 26, 33 - 38, 42 - 44, 46,
54, 59, 62 (19 problems)