inverse trigonometry functions and their derivatives · θ = sec-1x tan (sec-1x) = 7 csc ex 3...
TRANSCRIPT
![Page 1: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/1.jpg)
1
Inverse Trigonometry Functionsand Their Derivatives
![Page 2: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/2.jpg)
2
The graph of y = sin x does not pass the horizontal line test, so it has no inverse.
If we restrict the domain (to half a period), then we can talk about an inverse function.
![Page 3: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/3.jpg)
3
Definition
notation
EX 1 Evaluate these without a calculator.
a) c)
b) d)
![Page 4: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/4.jpg)
4
y = tan x y = sec x
Definition
[ ]
![Page 5: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/5.jpg)
5
EX 2 Evaluate without a calculator.
a) b) c)
![Page 6: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/6.jpg)
6
1
xθ
θ = cos-1x
sin(cos-1x) =
x
1θ sec (tan-1x) =
θ = tan-1x
x
1θ
θ = sec-1x
tan (sec-1x) =
![Page 7: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/7.jpg)
7
csc
EX 3 Calculate sin[2cos-1(1/4)] with no calculator.
Derivatives of Inverse Trig Functions
Let y = cos-1x. Find y'.
![Page 8: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/8.jpg)
8
C
C
EX 4
EX 5 Evaluate these integrals.
a)
b)
∈
![Page 9: Inverse Trigonometry Functions and Their Derivatives · θ = sec-1x tan (sec-1x) = 7 csc EX 3 Calculate sin[2cos-1(1/4)] with no calculator. Derivatives of Inverse Trig Functions](https://reader033.vdocuments.site/reader033/viewer/2022042318/5f079f757e708231d41de853/html5/thumbnails/9.jpg)
9