Transcript inverse function

Solving Right Triangles
Use trigonometric ratios to find angle
measures in right triangles and to solve
real-world problems.
Inverse Functions
 In
Algebra, when we have a function f(x)
such as y  2 x  3, we can find a function
1
called the inverse function f  x  by
exchanging places with the x and the y.
 In this case, if we exchange places with
the x and the y, we will get the following
function: x  2y  3 or change it to
x  3 which would be the inverse
y
function.
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Unit J
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Inverse Functions
 In
the previous lesson, we learned that the
trig function of sin 30º = 0.5.
 We want a function that will tell us that an
angle that has a sine of 0.5 would be 30º.
 This is written as sin-1 (0.5) = 30º and is
called an inverse function.
 For each of the three trigonometric functions,
there is an inverse function.
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Inverse Functions
O
 To find the inverse function for sin x 
think of
H
O
the angle as the x and the
as the y.
H

Now change places with the x and the y:
1  O 
sin    x
H 

To access the inverse trig functions on your
calculator use 2ND and then SIN , COS , or TAN .
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Key Concepts: Get Organized
C
5
4
A
Trig Function
sine
sin A =
cosine
cos A =
3
5
4
5
tan A =
3
4
tangent
3
B
Inverse Trig Function
3
5
cos-1 54
3
-1
tan 4
sin-1
Unit J
= m∠A
= m∠A
= m∠A
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Example of Inverse Functions
C
Use the given sides to find the
measure of angle A.
 You could use the sine, cosine or
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tangent function to find the answer.

sin A = ( 54 ) use: sin-1 ( 54 ) = 53º
cos A = ( 35 ) use: cos-1 ( 35 ) = 53º
B
5
A
3
tan A = ( 34 ) use: tan-1 ( 34 ) = 53º
No matter which function you use, you will get 53º.
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Inverse Functions

When you know the degrees of the angle and you
need to find the missing side, you will use one of
the functions: or.
A
O
O
cos x 
sin x 
tan x 
H
H
A

When you know the side lengths of the triangle
and you need to find a missing angle, we will use
one of the inverse functions:
1  O 
1  A 
1  O 
tan    x
cos    x
sin    x
 A
H 
H 
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Lesson Quiz
Use your calculator to find each angle measure to
the nearest degree.
1. cos-1(0.97) 14° 2. tan-1(2) 63° 3. sin-1(0.59) 36°
Find the unknown measures. Round lengths to the
nearest hundredth and angle measures to the
nearest degree.
4.
5.
AC  0.63; BC  2.37;
mB = 15°
Unit J
DF  5.7; mD  68°;
mF  22°
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