Degrees
What is $\sin 0^{\circ}$??
$$ 0 $$
What is $\sin 30^{\circ}$??
$$ \frac{1}{2} $$
What is $\sin 45^{\circ}$??
$$ \frac{\sqrt{2}}{2} $$
What is $\sin 60^{\circ}$??
$$ \frac{\sqrt{3}}{2} $$
What is $\sin 90^{\circ}$??
$$ 1 $$
What is $\cos 0^{\circ}$??
$$ 1 $$
What is $\cos 30^{\circ}$??
$$ \frac{\sqrt{3}}{2} $$
What is $\cos 45^{\circ}$??
$$ \frac{\sqrt{2}}{2} $$
What is $\cos 60^{\circ}$??
$$ \frac{1}{2} $$
What is $\cos 90^{\circ}$??
$$ 0 $$
What is $\tan 0^{\circ}$??
$$ 0 $$
What is $\tan 30^{\circ}$??
$$ \frac{\sqrt{3}}{3} $$
What is $\tan 45^{\circ}$??
$$ 1 $$
What is $\tan 60^{\circ}$??
$$ \sqrt{3} $$
What is $\tan 90^{\circ}$??
$$ \text{undefined} $$
For what values are $\sin$ and $\cos$ the same??
$$ 45^{\circ} $$
Which $\sin$ and $\cos$ values swap over??
$$ 30^{\circ}, 60^{\circ} $$
What is special about the value under the square root for sine $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$??
It goes $1$, $2$, $3$.
What is special about the value under the square root for cosine $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$??
It goes $3$, $2$, $1$.
Radians
What is $\sin 0$??
$$ 0 $$
What is $\sin \frac{\pi}{6}$??
$$ \frac{1}{2} $$
What is $\sin \frac{\pi}{4}$??
$$ \frac{\sqrt{2}}{2} $$
What is $\sin \frac{\pi}{3}$??
$$ \frac{\sqrt{3}}{2} $$
What is $\sin \frac{\pi}{2}$??
$$ 1 $$
What is $\cos 0$??
$$ 1 $$
What is $\cos \frac{\pi}{6}$??
$$ \frac{\sqrt{3}}{2} $$
What is $\cos \frac{\pi}{4}$??
$$ \frac{\sqrt{2}}{2} $$
What is $\cos \frac{\pi}{3}$??
$$ \frac{1}{2} $$
What is $\cos \frac{\pi}{2}$??
$$ 0 $$
What is $\tan 0$??
$$ 0 $$
What is $\tan \frac{\pi}{6}$??
$$ \frac{\sqrt{3}}{3} $$
What is $\tan \frac{\pi}{4}$??
$$ 1 $$
What is $\tan \frac{\pi}{3}$??
$$ \sqrt{3} $$
What is $\tan \frac{\pi}{2}$??
$$ \text{undefined} $$
What is special about the value under the square root for sine $\frac{\pi}{6}$, $\frac{\pi}{4}$ and $\frac{\pi}{3}$??
It goes $1$, $2$, $3$.
What is special about the value under the square root for cosine $\frac{\pi}{6}$, $\frac{\pi}{4}$ and $\frac{\pi}{3}$??
It goes $3$, $2$, $1$.
After how many radians does $\sin$ repeat??
$$ 2\pi $$
What’s another way of stating that $\sin$ repeats every $2\pi$ radians??
$$ \sin(\theta) = \sin(\theta + 2\pi) $$
After how many radians does $\cos$ repeat??
$$ 2\pi $$
What’s another way of stating that $\cos$ repeats every $2\pi$ radians??
$$ \cos(\theta) = \cos(\theta + 2\pi) $$
After how many radians does $\tan$ repeat??
$$ \pi $$
What’s another way of stating that $\tan$ repeats every $\pi$ radians??
$$ \tan(\theta) = \tan(\theta + \pi) $$
Because $\sin$ is the same going up as it comes down, what relation in radians can you write??
$$ \sin(x) = \sin(\pi - x) $$
General Rules
What’s another way of writing $\sin(-\theta)$??
$$ -\sin(\theta) $$
What’s another way of writing $-\sin(\theta)$??
$$ \sin(-\theta) $$
What’s another way of writing $\cos(-\theta)$??
$$ \cos(\theta) $$
2021-11-15
What’s $$\sin\left(\frac{\pi}{12}\right)$$??
$$ \frac{\sqrt{6} - \sqrt{2}}{4} $$
What’s $$\cos\left(\frac{\pi}{12}\right)$$??
$$ \frac{1 + \sqrt{3}}{2\sqrt{2}} $$
What’s $$\tan\left(\frac{\pi}{12}\right)$$??
$$ \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $$
Backlinks
Metadata
date: 2020-11-09 14:06
tags:
- '@?further-maths'
- '@?trigonometry'
- '@?school'
- '@?public'
- '@?a-level'
title: Further Maths - Trigonometry Values