Januar 21, 2020

von Jennette

Wie bewerten Sie $tan (\frac{π}{3})$ $tan (pi / 3)$ ?

Antworten:

$\sqrt{3}$ $sqrt3$

Erläuterung:

By evaluate I am assuming you mean give the $exact value$ $color(blue)" exact value"$

Obviously from a calculator the $tan (\frac{π}{3}) \approx 1.732$ $tan(pi/3)≈1.732$
But to obtain the exact value we can use the following $Exact value triangle$ $color(blue)" Exact value triangle"$

From this triangle we can obtain the exact values for sin/cos/tan of the angles $\frac{π}{3} and \frac{π}{6}$ $pi/3" and "pi/6$ . These are very useful and appear on many occasions so worth memorising for future use.

From triangle we obtain.

$tan (\frac{π}{3}) = \frac{\sqrt{3}}{1} = \sqrt{3}$ $tan(pi/3)=sqrt3/1=sqrt3$

For the same angle : $sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}, cos (\frac{π}{3}) = \frac{1}{2}$ $sin(pi/3)=sqrt3/2 , cos(pi/3)=1/2$