Question

Integral Trig Substitutions.

Answer 1

Where do the equations that are given to use the certain trig function in certain cases

Answer 2

if you have a proof , that's what im looking for

Answer 3

bascally you can test them after but i'm wondering how'd you do it with a triangle before guessing

Answer 4

I'm not sure what you mean, but see if the picture below helps you.

Answer 5

not quite i understand this it's where they get these rules

Answer 6

@.Sam.

Answer 7

in other words how'd they know to use sec,sin,and tan...

Answer 8

It depends on the question,
if its
\[a^2-x^2\]
Then from triangle

You know that
\[\sin(\theta)=\frac{x}{a} \\ \\ x=asin(\theta)\]

Answer 9

whered you get the triangle

Answer 10

basically i'm asking how do they get the triangle, is it simply guess and check or is there a way that if i don't remember these rules that i can use trig to find these

Answer 11

Its from \[a^2-x^2\]
Another example, if its \[a^2+x^2\] Notice the plus is given for adjacent side and opposite side, Pythagoras theorem.

then you get
\[x=atan(\theta)\]

Answer 12

I mean why do derivatives of certain cartesian functions yield a trig function

Answer 13

You need it only if you have something like this, you can use trig substitution for 1/sqrt(a^2+x^2). But that depends on the overall equation.

Answer 14

where does this come into play... for example you have the inverse of tan(x) yields a derivative of 1/x^2+1