# Tagged Questions

Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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### Seeking advice from the more experienced on which trig identities are crucial to memorize and which can be derived quickly

This is a bit of a two part question. I also have read some of the related questions, but I think mine is different as whether they can be derived quickly, rather than whether they can be derived, is ...
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### inequality $\sqrt{\cos x}>\cos(\sin x)$ for $x\in(0,\frac{\pi}{4})$

How can I prove the inequality $\sqrt{\cos x}>\cos(\sin x)$ for $x\in(0,\frac{\pi}{4})$ ? The derivative of $f(x):=\sqrt{\cos x}-\cos(\sin x)$ is very unpleasant, so the standard method is ...
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### What is the geometrical definition of the $\sec\theta$

This is the geometrical definition of the $\sec\theta$: My problem with this definition is when the angle $\theta$ is in the forth quadrant. The $\sec \theta$ is positive but the geometrical ...
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### How to calculate the shortest rotation from current to the target angle? [closed]

In the following situation: My current angle is 40*, my target angle is 130*. How should I calculate the rotation that should be done to reach the target angle from the current one? I've done the ...
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### How are the trigonometric ratios geometrically defined for non-acute angles?

The usual way trigonometric ratios are geometrically defined is always relative to an acute angle. So this way inside a right triangle, the trigonometric ratios are defined by the ratios of hypotenuse,...
### Help with the integral $\int x\sqrt{\frac{1-x^2}{1+x^2}}dx$
I would like to know what is $$\int x\sqrt{\frac{1-x^2}{1+x^2}}dx.$$ I put $x=\tan(y)$ to get integral of $\displaystyle \int \frac{\sin(y)}{\cos^3(y)}.\sqrt{\cos(2y)}dy$ I don't know whether \$\sin(x)...