Further Maths - Trigonometry Values


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 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 $3$, $2$, $1$.

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?

\[\pi\]

General Rules

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?

\[\sin(x) = \sin(\pi - x)\]

What’s another way of writing $\sin(-\theta)$?

\[-\sin(\theta)\]

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
\[\tan\left(\frac{\pi}{12}\right)\]

??

\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\]



Related posts