If $f(\theta )=sin(\theta )=0.1$, then find $f(\theta +\pi )=sin(\theta +\pi )$

Monserrat Sawyer
2022-05-29
Answered

If $f(\theta )=sin(\theta )=0.1$, then find $f(\theta +\pi )=sin(\theta +\pi )$

You can still ask an expert for help

vrhnjemuvs

Answered 2022-05-30
Author has **4** answers

You can do it by using the summation formula for sines

$\mathrm{sin}(x+y)=\mathrm{sin}(x)\mathrm{cos}(y)+\mathrm{sin}(y)\mathrm{cos}(x)$

just set $y=\pi $ and you get

$\begin{array}{rl}& \mathrm{sin}(x+\pi )=\mathrm{sin}(x)\mathrm{cos}(\pi )+\mathrm{sin}(\pi )\mathrm{cos}(x)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\mathrm{sin}(x)\left(-1\right)+0\mathrm{cos}(x)=-\mathrm{sin}(x)\end{array}$

$\mathrm{sin}(x+y)=\mathrm{sin}(x)\mathrm{cos}(y)+\mathrm{sin}(y)\mathrm{cos}(x)$

just set $y=\pi $ and you get

$\begin{array}{rl}& \mathrm{sin}(x+\pi )=\mathrm{sin}(x)\mathrm{cos}(\pi )+\mathrm{sin}(\pi )\mathrm{cos}(x)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\mathrm{sin}(x)\left(-1\right)+0\mathrm{cos}(x)=-\mathrm{sin}(x)\end{array}$

asked 2021-08-20

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

asked 2022-06-20

Fibonacci sequence can be described via the Binet's formula.

However, I was wondering if there was a similar formula for $n!$.

Is this possible? If not, why not?

However, I was wondering if there was a similar formula for $n!$.

Is this possible? If not, why not?

asked 2022-03-01

Finding a for $\mathrm{sin}(4a+\frac{\pi}{6})=\mathrm{sin}(2a+\frac{\pi}{5})$

asked 2022-06-02

In how many ways will the sum of the number of 1’s and 2’s (total of occurrences of 1's and 2's) equal the sum of the number of 3’s, 4’s, 5’s and 6’s, after n rolls, assuming n = 2i for some positive integer i? What is the probability of this occurring?

asked 2022-04-02

Prove that

$3{(\mathrm{sin}\theta -\mathrm{cos}\theta )}^{4}+6{(\mathrm{sin}\theta +\mathrm{cos}\theta )}^{2}+4({\mathrm{sin}}^{6}\theta +{\mathrm{cos}}^{6}\theta )-13=0$

asked 2022-06-20

Prove that ${\mathrm{cot}}^{n}\frac{\alpha}{2}+{\mathrm{cot}}^{n}\frac{\beta}{2}+{\mathrm{cot}}^{n}\frac{\gamma}{2}\ge {3}^{\frac{n+2}{2}}$

asked 2022-03-19

Calculate x, if

$\mathrm{tan}\left(x\right)=\mathrm{tan}9\mathrm{tan}69\mathrm{tan}33$