Exact Trig Values Flashcards

All 6 cards in this deck

What are the exact values of $\sin 30^\circ$, $\sin 45^\circ$ and $\sin 60^\circ$?

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

What are the exact values of $\cos 30^\circ$, $\cos 45^\circ$ and $\cos 60^\circ$?

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

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

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

What are the exact values of $\sin 0^\circ$, $\sin 90^\circ$, $\cos 0^\circ$ and $\cos 90^\circ$?

$\sin 0^\circ = 0$, $\sin 90^\circ = 1$, $\cos 0^\circ = 1$, $\cos 90^\circ = 0$

True or false? $\sin 30^\circ = \dfrac{\sqrt{3}}{2}$

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

What are the steps to find a side exactly using an exact trig value (no calculator)?

e.g. hypotenuse 6 cm, angle $30^\circ$, find the opposite side

1. Write the ratio: $\sin 30^\circ = \dfrac{x}{6}$
2. Replace with the exact value: $\dfrac{1}{2} = \dfrac{x}{6}$
3. Solve: $x = 6 \times \dfrac{1}{2} = 3$ cm