### Trigonometry: Compound Angles

Fluency exercise

Below are some function cards, some value cards, and some target cards. You may wish to print them out and cut them up, but keep them in the three separate piles.

You can choose a total of six cards, split between function cards and value cards in any way you choose (perhaps one or two function cards would be a good choice to start with). Choose your cards at random (pick from face-down cards, or get a friend to choose).

Then choose a random target card.

Your challenge is now to make the target by evaluating functions from your selected cards at values from your selected cards. You can use each card at most once (you don’t have to use them all).

For example, if you have the function card $\sin(\square + \square)$ and the value cards $\dfrac{\pi}{6}$ and $\dfrac{\pi}{3}$, then you could evaluate $\sin\left(\frac{\pi}{6} + \frac{\pi}{3}\right),$ but you would not be allowed to evaluate $\sin\left(\frac{\pi}{6} + \frac{\pi}{6}\right)$ (unless you happen to have two $\dfrac{\pi}{6}$ cards).

#### Function

$\sin(\square)$

#### Function

$\cos(\square)$

#### Function

$\tan(\square)$

#### Function

$\sin(\square + \square)$

#### Function

$\cos(\square + \square)$

#### Function

$\tan(\square + \square)$

#### Function

$\sin(\frac{\square}{2})$

#### Function

$\cos(\frac{\square}{2})$

#### Function

$\tan(\frac{\square}{2})$

#### Value

$0$

#### Value

$\dfrac{\pi}{6}$

#### Value

$\dfrac{\pi}{4}$

#### Value

$\dfrac{\pi}{3}$

#### Value

$\dfrac{\pi}{2}$

#### Value

$\dfrac{2\pi}{3}$

#### Value

$\dfrac{3\pi}{4}$

#### Value

$\pi$

#### Value

$-\dfrac{\pi}{6}$

#### Value

$-\dfrac{\pi}{4}$

#### Value

$-\dfrac{\pi}{3}$

#### Value

$-\dfrac{\pi}{2}$

#### Target

$0$

#### Target

$1$

#### Target

$\dfrac{1}{2}$

#### Target

$\dfrac{\sqrt{3}}{2}$

#### Target

$-\dfrac{1}{2}$

#### Target

$\dfrac{1}{\sqrt{3}}$

#### Target

$-\dfrac{\sqrt{3}}{2}$

#### Target

$\dfrac{\sqrt{2 - \sqrt{3}}}{2}$

#### Target

$\dfrac{1}{\sqrt{2}}$

#### Target

$-\sqrt{3}$

#### Target

$\sqrt{2}$

#### Target

$-\dfrac{1}{\sqrt{2}}$

#### Target

$-1$

#### Target

$-\sqrt{2}$