vegetars8t
2021-12-17
Answered

Derivative of $y=\mathrm{arccos}\left(x\right)$

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Evaluate the trigonmetric function at the given real number: $\mathrm{csc}\left(\frac{5\pi}{4}\right)$

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Given the following information about one trigonometric function, evaluate the other five functions.

$\mathrm{cos}u=\frac{5}{13}$ , where $0\le u\le \frac{\pi}{2}.$

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(a) Compute

(b) Verify the Cauchy-Schwarz inequality for the given pair of vector.

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Determine the greatest possible value of

$\sum _{i=1}^{10}\mathrm{cos}3{x}_{i}$

for real numbers$x}_{1},{x}_{2}\dots {x}_{10$ satisfying

$\sum _{i=0}^{10}{\mathrm{cos}x}_{i}=0$

My attempt:

$\sum \mathrm{cos}3x=\sum 4{\mathrm{cos}}^{3}x-\sum 3\mathrm{cos}x=4\sum {\mathrm{cos}}^{3}x$

So now we have to maximize sum of cubes of ten numbers when their sum is zero and each lie in interval [−1,1]. i often use AM GM inequalities but here are 10 numbers and they are not even positive. Need help to how to visualize and approach these kinds of questions.

for real numbers

My attempt:

So now we have to maximize sum of cubes of ten numbers when their sum is zero and each lie in interval [−1,1]. i often use AM GM inequalities but here are 10 numbers and they are not even positive. Need help to how to visualize and approach these kinds of questions.

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What is the derivative of $y=\mathrm{arcsin}\left(x\right)$ ?

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How do you solve $\mathrm{sin}2x=\mathrm{sin}x$ ?