Flashcards
2021-10-09
What is the $t$-substitution ($t = …$)??
$$ t = \tan^{-1}\left(\frac{\theta}{2}\right) $$
What is $\sin\theta$ in terms of $t$??
$$ \sin\theta = \frac{2t}{1 + t^2} $$
What is $\cos\theta$ in terms of $t$??
$$ \cos\theta = \frac{1 + t^2}{1 - t^2} $$
What is $\tan\theta$ in terms of $t$??
$$ \tan\theta = \frac{2t}{1 - t^2} $$
What triangle can you imagine for deriving the $t$-formulae??
2021-10-12
What $t$-substitution could you make other than $t = \tan\left(\frac{\theta}{2}\right)$ in order to rewrite $\sin 2\theta$??
$$ t = \tan \theta $$
$$ \sin 2\theta = \frac{1 + t^2}{2t} $$
What trick should jump for proving $$\sin^2 2\theta + \cos^2 2\theta = 1$$ with a $t$-substitution??
Using $t = \tan\theta$ rather than $t = \tan\left(\frac{\theta}{2}\right)$.
2022-01-20
What is in the numerator for the $t$-formulae involving $\cos$ and $\sin$??
$$ 1 + t^2 $$
If $$P(x) = 105 - 20\sin(6x) + 4\cos(12x)$$ and you were asked to make a substitution and find the derivative, what would be easier: taking the derivative and then making the substitution, or doing the substitution and then taking the derivative??
Taking the derivative and then making the substitution.
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date: 2021-10-09 18:49
tags:
- '@?public'
- '@?school'
- '@?further-maths'
- '@?further-pure-1'
title: Further Maths - T-formulae
