# Questions tagged [trigonometry]

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

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### Finding missing coordinate of a rectangle given an angle

The vertices of a right triangle are A (1,3,1), B(5,2,1), C(2,3,k). Angle A is 90 degrees. (a) Find k. (b) Find the angle C rounded to the nearest degree.
4answers
45 views

### If $a\sin(x) +b\sin(2x)+c\sin(3x)=0$ for every real $x$, then $a=b=c=0$.

How to solve the following without calculus? In a trigonometric manner. If $$a\sin(x) +b\sin(2x)+c\sin(3x)=0$$ for every real $x$, then $a=b=c=0$. I solved the problem by integrating and using the ...
1answer
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### How can one simplify $\sum_{n=1}^8\frac{\sin10n^\circ}{\cos5^\circ\cos10^\circ\cos20^\circ}$?

I have trouble solving the following question: Consider the following expression: $$\sum_{n=1}^8\frac{\sin10n^\circ}{\cos5^\circ\cos10^\circ\cos20^\circ}$$ The value of the above expression can be ...
2answers
47 views

### Why do we use the unit circle to solve for sin and cos

I know that in a unit circle where the radius is always one, sin is equal to y and cos is equal to x. But why do we use these values even when the radius or the hypothenuse of the triangle isn't equal ...
1answer
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2answers
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### $\tan \theta = -1 \pm \sqrt 6$ . What is the value of $\theta$ in degree?

I have got this : $\tan \theta = -1 \pm \sqrt 6$ in a problem. I have to find the value of $\theta$ in degree. Is there anyway we can find the angle in degree without using calculator ? I have no ...
2answers
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0answers
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1answer
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### Cosine modeling of a spot of paint on the wheel of a paddle-steamer

A paint spot $X$ lies on the outer rim of the wheel of a paddle-steamer. The wheel has radius $3$m and as it rotates at a constant rate, ${X}$ is seen entering the water every $4$ seconds. $H$ is the ...
1answer
104 views

### $\sum_{k=1}^{180^\circ}\cos\left(\frac{2\pi}{k}\right)$

How to compute $$\sum_{k=1}^{180}\cos\left(\frac{2\pi}{k}\right)$$ I have tried several ways to do it (including euler formula, etc), but all failed. The answer given by wolframalpha appeared to be a ...
3answers
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### Solve limit for a

Determine a so that: $\lim_{x\to0} \frac{\tan(ax)}{\sin(x)} = 2$ So far, I have used the L'hopital rule: $\frac{\frac{1}{a \cos(x)}}{\cos(x)} = \frac{1}{a \cos^3(x)} = 2$ But I am not sure if this is ...
1answer
51 views

### Not sure if this idea for calculating the square roots of a value has any merit

Okay, so I was thinking about square roots the other day and I spent some time thinking of how to visualize them: Say we have 10,000. The square root would be 100. So 100 of 100 equals 10,000. Now ...
2answers
52 views

### Generalizing Solutions for Trigonometric functions (Secant)

I have been working on the problem: $3\sec^2(2x)-5=1$ Where you have to solve for x and then enter the generalized solutions in ascending order. This is using the Acrobatiq platform, but I am ...
1answer
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### How do we solve the system of trigonometry equations?

I am unable to solve the following system of trig equations. My intention is to find the values of $x$ and $x_o$. $$6\cdot \sin(x) = 8\cdot \sin(x_o)$$ $$6\cdot \cos(x) + 8\cdot \cos(x_o) = 10$$ Here'...
2answers
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1answer
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### arg($1-e^{i\theta}$)

Im trying to calculate arg($1-e^{i\theta}$) for a problem im trying to solve but I have run across a slight problem: In this problem I have defined a branch cut to be $\mathbb{C}\setminus [1,\infty)$...
1answer
44 views

### Geometry(length of an angle bisector) [closed]

The length of two sides of a triangle are $b$ and $c$. Let $s$ be the length of the angle bisector of the angle between the two given sides. The length of the third side of the triangle is:
1answer
43 views

### How to solve $x\cos(t)+y\sin(t)=1$ for $t$

When trying to find the points, $P_1$ and $P_2$, on a circle of radius $R$ such that the tangent line to those points passes through the point $P_0$, it was all simple geometry until I ran into \$x\cos(...
1answer
55 views

### Bessel function approach as a trigonometric function

I was trying to find the eigenvalues, which is the positive roots of the equation bellow: $$J_{1}(a\lambda)Y_{1}(c\lambda) -J_{1}(c\lambda)Y_{1}(a\lambda) =0$$ I was presented with this trigonometric ...
2answers
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### How do I rewrite cos(-150) using a positive acute angle? [closed]

I need help to solve this. All of my answers I input are answered as incorrect. What am I doing wrong?
0answers
24 views

### How do I solve this question? (Trig) [closed]

I need help solving this, I solve it and the program marks it as wrong. question