bobbie71G
2021-08-16
Answered

Find exact value of $\mathrm{sin}495$ degrees without a calculator?

You can still ask an expert for help

rogreenhoxa8

Answered 2021-08-17
Author has **109** answers

For

asked 2021-08-20

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

asked 2022-02-28

I am stuck with the simple expression

$\frac{{\mathrm{cos}}^{2}(\theta +\alpha )}{1-{\mathrm{cos}}^{2}(\theta -\alpha )}=\text{const.}$

where$\theta$ is a variable and $\alpha$ is the number satisfying

$\alpha ={\mathrm{tan}}^{-1}\left(\frac{4}{3}\right)$

where

asked 2022-03-28

Determine the values of x,y such that $\mathrm{cos}x\mathrm{cos}z\mathrm{cos}y+\mathrm{sin}x\mathrm{sin}y<0$ for all z

asked 2022-01-16

Prove that $\mathrm{tan}}^{-1}\frac{\sqrt{1+{x}^{2}}+\sqrt{1-{x}^{2}}}{\sqrt{1+{x}^{2}}-\sqrt{1-{x}^{2}}}=\frac{\pi}{4}+\frac{1}{2}{\mathrm{cos}}^{-1}{x}^{2$ ?

Let the above expression be equal to$\varphi$

$\frac{\mathrm{tan}\varphi +1}{\mathrm{tan}\varphi -1}=\sqrt{\frac{1+{x}^{2}}{1-{x}^{2}}}$

$\frac{1+{\mathrm{tan}}^{2}\varphi +2\mathrm{tan}\varphi}{1+{\mathrm{tan}}^{2}\varphi -2\mathrm{tan}\varphi}=\frac{1+{x}^{2}}{1-{x}^{2}}$

$\frac{1+{\mathrm{tan}}^{2}\varphi}{2\mathrm{tan}\varphi}=\frac{1}{{x}^{2}}$

$\mathrm{sin}2\varphi ={x}^{2}$

$\varphi =\frac{\pi}{4}-\frac{1}{2}{\mathrm{cos}}^{-1}{x}^{2}$

Where am I going wrong?

Let the above expression be equal to

Where am I going wrong?

asked 2021-12-30

Why does $\sum _{i=1}^{k}\mathrm{sin}\left(i\frac{2\pi}{k}\right)=0$ for integers k

asked 2022-04-26

Simplifying, I have

$\frac{1}{\mathrm{sin}x\mathrm{cos}x}=3$

asked 2022-03-31

prove that maximum value of $\mathrm{cos}\alpha \mathrm{cos}\beta$ occurs when $\alpha =\beta =\frac{\sigma}{2}$

If$\alpha ,\beta \in (0,\frac{\pi}{2})$ and $\alpha +\beta =\sigma$ (constant), then prove that maximum value of $\mathrm{cos}\alpha \mathrm{cos}\beta$ occurs when $\alpha =\beta =\frac{\sigma}{2}$

If