kramtus51

2022-01-03

Find , and $\frac{\mathrm{tan}x}{2}$ from the given information.

jgardner33v4

Given data:
The trigonometry function is $\mathrm{tan}\left(x\right)=2\sqrt{2}$.
Then the interval ${0}^{\circ }
Solve the trigonometry function $\mathrm{tan}\left(x\right)=2\sqrt{2}$
$\mathrm{tan}\left(x\right)=2\sqrt{2}$
$x={\mathrm{tan}}^{-1}\left(2\sqrt{2}\right)$
$={70.528}^{\circ }$

temnimam2

Substitute the values in expression $\mathrm{sin}\left(\frac{x}{2}\right)$ and evaluate,
$\mathrm{sin}\left(\frac{x}{2}\right)=\mathrm{sin}\left(\frac{{70.528}^{\circ }}{2}\right)$
$=\mathrm{sin}\left({35.264}^{\circ }\right)$
$=0.577$
Hence the value of $\mathrm{sin}\left(\frac{x}{2}\right)$ is 0.577.

karton

Substitute the values in expression $\mathrm{cos}\left(\frac{x}{2}\right)$ and evaluate,
$\mathrm{cos}\left(\frac{x}{2}\right)=\mathrm{cos}\left(\frac{{70.528}^{\circ }}{2}\right)$
$=\mathrm{cos}\left({35.264}^{\circ }\right)$
$=0.816$
Hence the value of $\mathrm{cos}\left(\frac{x}{2}\right)$ is 0.816.
Substitute the values in expression $\mathrm{tan}\left(\frac{x}{2}\right)$ and evaluate,
$\mathrm{tan}\left(\frac{x}{2}\right)=\mathrm{tan}\left({35.264}^{\circ }\right)$
$=0.707$
Hence the value of $\mathrm{tan}\left(\frac{x}{2}\right)$ is 0.707.

Do you have a similar question?