Further Maths - Trigonometry Values
Degrees
Which $\sin$ and $\cos$ values swap over?
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 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 $3$, $2$, $1$.
What’s another way of stating that $\sin$ repeats every $2\pi$ radians?
What’s another way of stating that $\cos$ repeats every $2\pi$ radians?
General Rules
What’s another way of stating that $\tan$ repeats every $\pi$ radians?
Because $\sin$ is the same going up as it comes down, what relation in radians can you write?
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
\[\tan\left(\frac{\pi}{12}\right)\]??
\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\]