# 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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### meaning of powers on trig functions

I always forget this, when a trig function has an exponent does that mean multiply itself or apply itself to the result recursivly? e.g. does $\sin(x)^2=\sin(x)\sin(x)$ or $=\sin(\sin(x))$? What ...
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### What is the difference between the geometric and trigonometric definition of an angle?

I vaguely remember reading that there is a difference between the geometric definition of an angle and the trigonometric definition of an angle. I've tried to search everywhere I can think of but I ...
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### How to solve $a \cos \alpha + b \sin \alpha = c$ for $\alpha$?

I'm solving a physics problem and I came down to solving an equation of the form $$a \cos \alpha + b \sin \alpha = c$$ Can someone help me to solve this? Thanks in advance!
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### Product of projections of equispaced rotating vector

When equal and equi-spaced forces are summed on y-axis what is vector sum? How do we derive the formula $$\sum_{k=1}^{n-1}\sin\frac{\pi k}{n} = \cot \frac{\pi}{2 n}$$ ( Formula given by ...
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### Bearing of a line or a point

Rochelle is 25 miles due south of Rockford,and North Chicago is 65 miles due east of Rockford.Find the bearing of North Chicago From Rochelle. I used Pythagorean theorem in solving this because i ...
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### Geometric proof of $\frac{\sin{60^\circ}}{\sin{40^\circ}}=4\sin{20^\circ}\sin{80^\circ}$

It is well-known that $$\sin{20^\circ}\sin{40^\circ}\sin{80^\circ}=\frac{\sqrt{3}}{8}$$ It follows that $$\frac{\sin{60^\circ}}{\sin{40^\circ}}=4\sin{20^\circ}\sin{80^\circ}$$ But how to prove this by ...
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### In an equilateral spherical triangle, show that SecA=1+Seca

Q. In an equilateral spherical triangle, show that $SecA=1+Seca$ So A is the vertex or the angle of the triangle and a is the side of the equilateral spherical triangle. I started off the proof by ...
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### How to solve $dx = (\sin y + 3 \cos y + x) dy$

How could I solve this? I guess I need to use integration factor, but I do not understand it very well. $dx = (\sin y + 3 \cos y + x) dy$