Exact Values Flashcards

All 8 cards in this deck

What are the exact values of $\sin\theta$ for $\theta = 0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ$?

$\sin 0^\circ = 0$, $\sin 30^\circ = \frac{1}{2}$, $\sin 45^\circ = \frac{1}{\sqrt{2}}$, $\sin 60^\circ = \frac{\sqrt{3}}{2}$, $\sin 90^\circ = 1$

What are the exact values of $\cos\theta$ for $\theta = 0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ$?

$\cos 0^\circ = 1$, $\cos 30^\circ = \frac{\sqrt{3}}{2}$, $\cos 45^\circ = \frac{1}{\sqrt{2}}$, $\cos 60^\circ = \frac{1}{2}$, $\cos 90^\circ = 0$

What are the exact values of $\tan\theta$ for $\theta = 0^\circ, 30^\circ, 45^\circ, 60^\circ$?

$\tan 0^\circ = 0$, $\tan 30^\circ = \frac{1}{\sqrt{3}}$, $\tan 45^\circ = 1$, $\tan 60^\circ = \sqrt{3}$

True or false? $\sin 60^\circ = \cos 30^\circ$

True.
Both are equal to $\frac{\sqrt{3}}{2}$.

True or false? $\cos 60^\circ = \frac{\sqrt{3}}{2}$

False.
$\cos 60^\circ = \frac{1}{2}$; $\frac{\sqrt{3}}{2}$ is $\cos 30^\circ$.

What are the steps to add or subtract multiples of $\pi$ exactly?
e.g. $2\pi + 5\pi$

1. Treat $\pi$ like a letter term: $2\pi + 5\pi$
2. Add (or subtract) the numbers in front: $2 + 5 = 7$
3. Write the answer as a multiple of $\pi$: $7\pi$

What does it mean to give an answer as an exact value?

The answer is left as a fraction, surd or multiple of $\pi$, not as a rounded decimal.
e.g. $\frac{1}{3}$, not $0.33$

True or false? Writing $\frac{2}{3}$ as $0.67$ gives an exact answer.

False. $0.67$ is rounded; the exact answer is the fraction $\frac{2}{3}$.