Trig Rules for Subsitution Flashcards
1
Q
what can a and x equal for the triangle
A
a = adjacent or hypotenuse
x = opposite or hypotenuse
2
Q
√(a² - x²)
A
a = hypotenuse
x = opposite
3
Q
√(a² + x²)
A
a = adjacent
x = opposite
4
Q
√(x² - a²)
A
a = adjacent
x = hypotenuse
5
Q
∫sin³(x)cos⁴(x)dx
sin = odd, cos = even
A
∫sin²(x)cos⁴(x)sin(x)dx
use sin²(x) identity
6
Q
∫sin⁴(x)cos³(x)dx
sin = even, cos = odd
A
∫sin⁴(x)cos²(x)cos(x)dx
use cos²(x) identity
7
Q
∫sin⁴(x)cos⁴(x)dx
sin = even, cos= even
A
Use sin²(x) = (1 - cos(2x))/2 or
Use cos²(x) = (1 + cos(2x))/2
Will need repeated uses
8
Q
∫sec⁴(x)tan⁴(x)dx
sec = even, tan = even or odd
A
∫sec²(x)tan⁴(x)sec²(x)dx
use sec²(x) identity
9
Q
∫sec⁴(x)tan³(x)dx
sec = even or odd tan = odd
A
∫sec³(x)tan²(x)tan(x)sec(x)dx
use tan²(x) identity
