Page 205 - Calculus Demystified

CHAPTER 6
192
y Transcendental Functions

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x
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Fig. 6.26

Summary of Key Facts About the Inverse Trigonometric Functions
π π
Sin x = sin x, − ≤ x ≤ ; Cos x = cos x, 0 ≤ x ≤ π;
2 2
π π
Tan x = tan x, − <x < ; Cot x = cot x, 0 <x <π;
2 2
Sec x = sec x, x ∈[0,π/2) ∪ (π/2,π]; Csc x = csc x, x ∈[−π/2, 0) ∪ (0,π/2].
d −1 1 d −1 1
Sin x = √ , −1 <x < 1; Cos x =−√ , −1 <x < 1;
dx 1 − x 2 dx 1 − x 2
d −1 1 d −1 1
Tan x = , −∞ <x < ∞; Cot x =− , −∞ <x < ∞;
dx 1 + x 2 dx 1 + x 2
d −1 1 d −1 1
Sec x = √ , |x| > 1; Csc x =− √ , |x| > 1;
dx |x|· x − 1 dx |x|· x − 1
2
2

du −1 du −1
√ = Sin u + C; √ =−Cos u + C;
1 − u 2 1 − u 2

du −1 du −1
du = Tan u + C; du =−Cot u + C;
1 + u 2 1 + u 2

du −1 du −1
√ = Sec u + C; √ =−Csc u + C.
2
2
|u|· u − 1 |u|· u − 1
You Try It: What is the derivative of Sec −1 2
x ?