Write an equation in terms of x and y for the function that is described by the given characteristics. A sine curve with a period of

Tahmid Knox
2021-08-18
Answered

Write an equation in terms of x and y for the function that is described by the given characteristics. A sine curve with a period of

You can still ask an expert for help

Jozlyn

Answered 2021-08-19
Author has **85** answers

The graph of

Use the sine function:

The period is

The phase shift is

or

asked 2022-11-17

Evaluating $\int \frac{dx}{\mathrm{cos}x-1}$

I was wondering if my solution to the integral:

$\int \frac{dx}{1-\mathrm{cos}x}$

is legit?

$\int \frac{1}{\mathrm{cos}x-1}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=\int -\frac{1}{2}\cdot \frac{1}{{\mathrm{sin}}^{2}\left(\frac{x}{2}\right)}=\frac{1}{2}\int -\mathrm{csc}\left(\frac{1}{2}x\right)\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=\overline{){\displaystyle \mathrm{cot}\left(\frac{1}{2}x\right)+C}}\phantom{\rule{0ex}{0ex}}{(\mathrm{cot}\left(\frac{1}{2}x\right))}^{\prime}=-{\mathrm{csc}}^{2}\left(\frac{1}{2}x\right)\cdot \frac{1}{2}=\overline{){\displaystyle -\frac{1}{2}{\mathrm{csc}}^{2}\left(\frac{1}{2}x\right)}}\phantom{\rule{0ex}{0ex}}\mathrm{cos}x-1=\mathrm{cos}x-\mathrm{cos}(0)=-2\mathrm{sin}\left(\frac{x+0}{2}\right)\mathrm{sin}\left(\frac{x-0}{2}\right)=-2{\mathrm{sin}}^{2}\left(\frac{x}{2}\right)$

My solution is based around the fact that the derivative of $\mathrm{cot}x$ is $-{\mathrm{csc}}^{2}x$. I basically converted $\mathrm{cos}x-1$ to $\mathrm{cos}x-\mathrm{cos}0$ and from there used the $\mathrm{cos}a-\mathrm{cos}b$ trig identity.

I was wondering if my solution to the integral:

$\int \frac{dx}{1-\mathrm{cos}x}$

is legit?

$\int \frac{1}{\mathrm{cos}x-1}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=\int -\frac{1}{2}\cdot \frac{1}{{\mathrm{sin}}^{2}\left(\frac{x}{2}\right)}=\frac{1}{2}\int -\mathrm{csc}\left(\frac{1}{2}x\right)\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=\overline{){\displaystyle \mathrm{cot}\left(\frac{1}{2}x\right)+C}}\phantom{\rule{0ex}{0ex}}{(\mathrm{cot}\left(\frac{1}{2}x\right))}^{\prime}=-{\mathrm{csc}}^{2}\left(\frac{1}{2}x\right)\cdot \frac{1}{2}=\overline{){\displaystyle -\frac{1}{2}{\mathrm{csc}}^{2}\left(\frac{1}{2}x\right)}}\phantom{\rule{0ex}{0ex}}\mathrm{cos}x-1=\mathrm{cos}x-\mathrm{cos}(0)=-2\mathrm{sin}\left(\frac{x+0}{2}\right)\mathrm{sin}\left(\frac{x-0}{2}\right)=-2{\mathrm{sin}}^{2}\left(\frac{x}{2}\right)$

My solution is based around the fact that the derivative of $\mathrm{cot}x$ is $-{\mathrm{csc}}^{2}x$. I basically converted $\mathrm{cos}x-1$ to $\mathrm{cos}x-\mathrm{cos}0$ and from there used the $\mathrm{cos}a-\mathrm{cos}b$ trig identity.

asked 2022-01-21

How do you simplify

${\mathrm{tan}}^{2}4b-{\mathrm{sec}}^{2}4b$

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Express $\mathrm{sin}\left(\mathrm{arccos}\left(\frac{2}{x}\right)\right)$ in terms of x.

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h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.

h(x)=|x+3|−5.

h(x)=|x+3|−5.

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find the exact value of

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Find the derivative of $f\left(x\right)=\sqrt{x}$ .

asked 2022-11-10

How many solutions exist to this trig relation?

$$\mathrm{sin}\left(\frac{1}{2}\theta \right)=2\mathrm{cos}\left(2\theta \right)$$

$$\mathrm{sin}\left(\frac{1}{2}\theta \right)=2\mathrm{cos}\left(2\theta \right)$$