Question

- Use the unit circle to evaluate the six trigonometric functions of theta= 4pi

Answer 1

The six trigonometric functions, $\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$, $\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$,$\tan \dfrac{\pi}{4} =1$, $\cot \dfrac{\pi}{4} =1$, $\sec \dfrac{\pi}{4} =\sqrt{2}$ and $\csc \dfrac{\pi}{4} =\sqrt{2}$.

Step-by-step explanation:

We have,

$\dfrac{\pi}{4}$

To write the six trigonometric functions = ?

$\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$

$\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$

$\tan \dfrac{\pi}{4} =1$

$\cot \dfrac{\pi}{4} =1$

$\sec \dfrac{\pi}{4} =\sqrt{2}$

$\csc \dfrac{\pi}{4} =\sqrt{2}$

∴ The six trigonometric functions, $\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$, $\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$,$\tan \dfrac{\pi}{4} =1$, $\cot \dfrac{\pi}{4} =1$, $\sec \dfrac{\pi}{4} =\sqrt{2}$ and $\csc \dfrac{\pi}{4} =\sqrt{2}$.