What is arccos 1/2?

spremani0r
2022-09-14
Answered

What is arccos 1/2?

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

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Writing ${\mathrm{tan}}^{2}\left(2{\mathrm{sec}}^{-1}\left(\frac{x}{3}\right)\right)$ in algebraic form

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Find the limit $\underset{x\to \frac{\pi}{2}}{lim}\left(\frac{\mathrm{cos}\left(5x\right)}{\mathrm{cos}\left(3x\right)}\right)$ without using L'Hospital's rule

asked 2022-05-28

I need to find the limit for $x\in \mathbb{R}$

$\underset{n\to \mathrm{\infty}}{lim}\sum _{k=0}^{n}|{e}^{ixk/n}-{e}^{ix(k-1)/n}|$

Using Euler's formula and cosine of a sum this simplifies to

$\underset{n\to \mathrm{\infty}}{lim}n\sqrt{2(1-\mathrm{cos}(x/n))}$

$\underset{n\to \mathrm{\infty}}{lim}\sum _{k=0}^{n}|{e}^{ixk/n}-{e}^{ix(k-1)/n}|$

Using Euler's formula and cosine of a sum this simplifies to

$\underset{n\to \mathrm{\infty}}{lim}n\sqrt{2(1-\mathrm{cos}(x/n))}$

asked 2022-07-28

In A and B, cosine is given..find sine and tangent if x liesin the specific interval.

A.) $\mathrm{cos}(x)=1/3x\in [\pi /2,0]$

B.) $\mathrm{cos}(x)=-5/13x\in [\pi /2,\pi ]$

C.) $s=\mathrm{sec}(\pi x/2)$...Find the period. What symmetries does the function have?

D.) $\mathrm{cos}(x+\pi /4)-1$. What is the period?

A.) $\mathrm{cos}(x)=1/3x\in [\pi /2,0]$

B.) $\mathrm{cos}(x)=-5/13x\in [\pi /2,\pi ]$

C.) $s=\mathrm{sec}(\pi x/2)$...Find the period. What symmetries does the function have?

D.) $\mathrm{cos}(x+\pi /4)-1$. What is the period?

asked 2022-01-27

Find the least value for $\mathrm{sin}x-{\mathrm{cos}}^{2}x-1$

At first I found the first derivative to be${y}^{\prime}=\mathrm{cos}x+2\mathrm{sin}x\mathrm{cos}x$

Critical point$0,-\frac{\pi}{6}$ (principal)

$y-\mathrm{sin}x+2\left(\mathrm{cos}2x\right)$

Then substitution of x by critical points I found minima. But my answer is incorrect.

Correct minimum value is$-\frac{9}{4}$

At first I found the first derivative to be

Critical point

Then substitution of x by critical points I found minima. But my answer is incorrect.

Correct minimum value is