Mathematics Stack Exchange
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Questions tagged [trigonometry]

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

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles.

Trigonometry is most simply associated with planar right-angle triangles. The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles.

One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles.

See Wikipedia's list of trigonometric identities.

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Unclear step in half-angle formula derivation (trigonometric identities)

In deriving the half-angle formulas, my textbook first says: "Let's take the following identities:" $$\cos^2\left(\frac a2\right)+\sin^2\left(\frac a2\right)=1;$$ $$\cos^2\left(\frac a2\right)-\sin^2\left(\frac a2\right)=\cos(a);$$ These identities…
CopperKettle
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Simplify a trigonometric equation

UPDATE **** AGGGH, I am embarrassed, but I made an error in deriving the equation in this question. Please disregard this question, and I will start a new one if I get stuck on the corrected version. It does appear that @avz2611's hint may still…
alfreema
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Can one generate all possible binary strings by sampling a trig function at regular intervals?

I'm using a trigonometric function to generate binary strings by sampling the function at regular intervals and mapping each sample value to a binary bit. As a simple example: if the function is $g(x)=sin(fx)$, and I need a 4-bit binary string, I…
SnagaDuath
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How to solve the trigonometric equation $\cos17x=20\cos x$?

How to solve the following trigonometric equation? $$\cos17x=20\cos x$$ I'm really awful in trigonometry. I tried division of both sides by $20$. Thanks.
MelanieJohansson
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$2\cos(x)+x=0$? Advanced trig. question.

Title says it all: $$2\cos(\theta)+(\theta)=0$$ the interval should be between $0$ to $2\pi$. Been trying to figure this out for quite a while, still no luck. I'm trying to find if the solution exists or not.
Kapooky Handy
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Trigonometric curiosity

How prove this $$-\tan\frac{10\pi}{41}+4\left(\sin\frac{2\pi}{41}+\sin\frac{4\pi}{41}+\sin\frac{12\pi}{41}+\sin\frac{20\pi}{41}-\sin\frac{26\pi}{41}-\sin \frac{30\pi}{41}\right)=…
user178256
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If $y = a\sin{x} + b\cos{x} +C$ then find maxima and minima for $y$.

I was able to solve it till $$y = \sqrt{(a^2 + b^2)}\sin(\alpha + x) + C.$$ But I don't know how to find maxima and minima from here. If $C = 0$ then maxima & minima equals the amplitude of the sine curve but when $C$ is non-zero then? I need help…
Shubham
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how to prove that $\sin(90+v) = \cos(v)$

I need to prove that $\sin(90+v) = \cos v$ and that $\cos(90+v) = -\sin v$ So I did the following steps to prove these statements $\sin(90+v) = \sin(90-(-v)) = \cos(-v) = \cos(v)$ $\cos(90+v) = \cos(90-(-v)) = \sin(-v) = -\sin(v)$ Is this…
Sejad Dulic
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Equilateral Triangle Problem With Trig

I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle P. The distance $|AP|=3 cm, |BP|=4 cm, |CP|=5 cm.$ What is the area of the triangle? I have seen this problem posted here before…
Lionblaze16
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Solve for Theta: $a = b\tan(\theta) - \frac{c}{\cos(\theta)}$

The title pretty much sums it up. How do I solve for $\theta$ given the following equation. $a = b\tan(\theta) - \frac{c}{\cos(\theta)}$ I am not a student and this is not homework. It's been quite a while since I've done any significant trig and…
Kyle
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Solve the trigonometric equation/inequality

$(1).\quad\cos^2(2x) + \sin^4(x) = 2$ $($solve the equation$)$ $(2).\quad2\cos^2(3x) + 5\cos(3x) - 3 < 0$. For this question, I tried letting $t=\cos(3x)$. Thus, $2t^2 + 5t - 3< 0$, but that doesn't factor properly. I'm really stuck... It…
mathemator
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Applying angle addition formulas for subtraction

The angle addition formula says that: $\sin(\phi + \theta) = \sin(\phi) \cdot \cos(\theta) + \cos(\phi) \cdot \sin(\theta)$ Why are the following steps valid?: $\sin(\phi − \theta) = \sin(\phi) \cdot \cos(−\theta) + \cos(\phi) \cdot \sin(−\theta)=…
Jeremy
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When is $\cos (x) \geq \frac{1}{2}$?

When is $\cos (x) \geq \frac{1}{2}$? I know the function repeats, so I know I should end up with an interval that allows for integer multiples. e.g. something like this (but obviously not this exactly) $[0 + n, \pi + n]$.
user174606
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Unconventional way to solve trig question

I was working on a trig question and got stuck, but then I noticed a possible way to solve the problem. However, this way seemed to be slightly unconventional and possibly not what the book was looking for. The question was: "Find $k$ and $b$ when…
E.O.
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Find the angle of a triangle

I'v tried to solve this problem but did not get the right result. Triangel PQR is PQ = 5,0 cm, QR = 6,3 cm and RP = 7,4 cm. Calculate angle P. I tried to solve it by using by using the following formula $c^2 = a^2 + b^2 - 2abcosP$. The result I get…
S4M1R
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