# Further Maths - T-formulae

## Flashcards

### 2021-10-09

What is the $t$-substitution ($t = …$)?

What is $\sin\theta$ in terms of $t$?

What is $\cos\theta$ in terms of $t$?

What is $\tan\theta$ in terms of $t$?

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 $\sin 2\theta$?

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 $\sin$?

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.