Cem Hayes
2021-08-19
Answered

Solve the equations and show all the solutions in the first quadrant

$3\mathrm{tan}\theta -\mathrm{cot}\theta =0$

You can still ask an expert for help

Nichole Watt

Answered 2021-08-20
Author has **100** answers

Use the trigonometry ratio

$3\mathrm{tan}\theta -\mathrm{cot}\theta =0$

$\Rightarrow 3\mathrm{tan}\theta =\mathrm{cot}\theta$

$\Rightarrow \frac{3\mathrm{tan}\theta}{\mathrm{cot}\theta}=1$

$\Rightarrow \mathrm{tan}\pm \theta =\frac{1}{\sqrt{3}}$

$\Rightarrow \theta ={\mathrm{tan}}^{-1}(\pm \frac{1}{\sqrt{3}})$

$=\pm {\mathrm{tan}}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$=\pm \frac{\pi}{6}$

Solutioms in the first quadrant is$\theta =\frac{\pi}{6}$

Solutioms in the first quadrant is

Jeffrey Jordon

Answered 2021-12-10
Author has **2027** answers

Answer is given below (on video)

asked 2021-08-20

Let P(x, y) be the terminal point on the unit circle determined by t. Then

asked 2022-01-16

Integrate from 0 to $2\pi$ with respect to $\theta$ the following $(\mathrm{sin}\theta +\mathrm{cos}\theta )}^{n$

asked 2022-04-29

If $\mathrm{sin}2x=\frac{5}{13}$ and $0}^{\circ}<x<{45}^{\circ$ , find $\mathrm{sin}x$ and $\mathrm{cos}x$ .

asked 2022-04-26

Simplify the equation $16{\mathrm{cos}}^{6}\left(t\right)+16{\mathrm{sin}}^{6}\left(t\right)+48{\mathrm{sin}}^{2}\left(t\right){\mathrm{cos}}^{2}\left(t\right)$

asked 2022-01-23

Proving $\int}_{0}^{\frac{\pi}{4}}{\mathrm{sin}}^{n}\left(x\right)dx>\frac{1}{{2}^{\frac{n}{2}}(n+2)$

asked 2022-04-29

Prove that:

$\sqrt{2}{\mathrm{sin}10}^{\circ}+\sqrt{3}{\mathrm{cos}35}^{\circ}={\mathrm{sin}55}^{\circ}+2{\mathrm{cos}65}^{\circ}$

asked 2022-01-27

Why

By orthogonality, we know that

But the above quantity is 0 even if n=1. Shouldn't it be