Trig-substitutions → Trig Rule
Last updated
Last updated
The goal is to simplify expression by CONVERTING terms of
x
into simplified expression in terms ofθ
.
How to do this? We can identify some trigonometric patterns in the expression and apply the Pythagorean Theorem
.
Solve:
In this expression, we can easily identify there is a "pythagorean-like terms":
We can see x
and 2
as two sides of a triangle:
Once we identify the pattern, we can easily get some information out of it in terms of θ
:
From the information tan(θ)=x/2
we can get the relationship between x & θ
, which is: x=2tan(θ)
And now we can convert the original expression to be in terms of θ
:
Solve: ...