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What is $\int_0^{\pi/2}\sin^7(\theta)\cos^5(\theta)d\theta$

score 6.5k · Answer 1 · 2026-04-13 13:30:30

6.5k

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What is $\int_0^{\pi/2}\sin^7(\theta)\cos^5(\theta)d\theta$

Published on 13 Apr 2026 - 13:30

score 818 · Answer 2 · 2026-04-16 01:59:44

818

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Evaluate $\sum_{n=1}^\infty \arctan\left(\frac{1}{8n^2} \right)$

Published on 16 Apr 2026 - 1:59

score 73 · Answer 3 · 2026-04-14 10:46:12

73

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The function $f(x)=\arcsin(a\sinh(\sin(x)))$

Published on 14 Apr 2026 - 10:46

score 160 · Answer 4 · 2026-04-15 00:17:06

160

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Maximizing the area of a cyclic trapezoid whose long base is the circumdiameter. Non-trigonometric solution?

Published on 15 Apr 2026 - 0:17

score 104 · Answer 5 · 2026-04-13 11:55:22

104

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Proving that $\cos\left(ax-\frac{b\pi}{2}\right)=\sin(ax)$ for all $a$, $b$

Published on 13 Apr 2026 - 11:55

score 33 · Answer 6 · 2026-04-15 22:36:21

33

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To specify $a,b,k$ in $a\cos(kx)+b$

Published on 15 Apr 2026 - 22:36

score 155 · Answer 7 · 2026-04-16 21:52:39

155

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Non zero solution of $3x\cos(x) + (-3 + x^2)\sin(x)=0$

Published on 16 Apr 2026 - 21:52

score 275 · Answer 8 · 2026-04-17 08:58:57

275

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Possible to prove that a particular trigonometric expression is always positive?

Published on 17 Apr 2026 - 8:58

score 1k · Answer 9 · 2026-04-14 15:18:25

1k

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Proof that $\sin {x}$ is infinitely continuously differentiable over $[m,n]$

Published on 14 Apr 2026 - 15:18

score 1.4k · Answer 10 · 2026-04-14 19:00:26

1.4k

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Cancelling with absolute values

Published on 14 Apr 2026 - 19:00

score 558 · Answer 11 · 2026-04-16 10:37:30

558

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Solving for $x$ in $\sin^{-1}(2x) + \sin^{-1}(3x) = \frac \pi 4$

Published on 16 Apr 2026 - 10:37

score 195 · Answer 12 · 2026-04-15 02:31:46

195

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Find the Range and Inverse of the function $f(x)=\sec x\tan x+\sec^2 x$

Published on 15 Apr 2026 - 2:31

score 850 · Answer 13 · 2026-04-10 20:06:09

850

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How to solve for $\theta$ in terms of $a,b,c$ in this expression?

Published on 10 Apr 2026 - 20:06

score 548 · Answer 14 · 2026-04-16 13:27:02

548

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What is the value of: $\lim_{n\rightarrow \infty}\sum_{r=1}^{n-1}\frac{\cot^2(r\pi/n)}{n^2}$

Published on 16 Apr 2026 - 13:27

score 155 · Answer 15 · 2026-04-15 03:46:48

155

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Error in proving Lagrange's Identity for $1+\cos\theta+\cdots+\cos n\theta$

Published on 15 Apr 2026 - 3:46

List Question

What is $\int_0^{\pi/2}\sin^7(\theta)\cos^5(\theta)d\theta$

Evaluate $\sum_{n=1}^\infty \arctan\left(\frac{1}{8n^2} \right)$

The function $f(x)=\arcsin(a\sinh(\sin(x)))$

Maximizing the area of a cyclic trapezoid whose long base is the circumdiameter. Non-trigonometric solution?

Proving that $\cos\left(ax-\frac{b\pi}{2}\right)=\sin(ax)$ for all $a$, $b$

To specify $a,b,k$ in $a\cos(kx)+b$

Non zero solution of $3x\cos(x) + (-3 + x^2)\sin(x)=0$

Possible to prove that a particular trigonometric expression is always positive?

Proof that $\sin {x}$ is infinitely continuously differentiable over $[m,n]$

Cancelling with absolute values

Solving for $x$ in $\sin^{-1}(2x) + \sin^{-1}(3x) = \frac \pi 4$

Find the Range and Inverse of the function $f(x)=\sec x\tan x+\sec^2 x$

How to solve for $\theta$ in terms of $a,b,c$ in this expression?

What is the value of: $\lim_{n\rightarrow \infty}\sum_{r=1}^{n-1}\frac{\cot^2(r\pi/n)}{n^2}$

Error in proving Lagrange's Identity for $1+\cos\theta+\cdots+\cos n\theta$

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