Solving Trigonometry Problems: Basic, Advanced & Examples

High School
Geometry
Trigonometry

How do you simplify
$\tan^{2} 4 b - \sec^{2} 4 b$

iocasq4 2022-01-21

What is $\sin (2 \arcsin (\frac{3}{5}))$ ?

blitzbabeiy 2022-01-21

How do you calculate $\tan (\arccos (\frac{5}{13}))$ ?

veceriraby 2022-01-21

Prove in detail the inequality of this formula:
Let x, y, z positive real number and $△ A B S$ a triangle. $[A B C]$ denotes the triangle area and a, b, c the sides of the triangle. The inequality below is true:
$a^{2} x + b^{2} y + c^{2} z \geq 4 [A B C] \sqrt{x y + x z + y z}$

Ernest Ryland 2022-01-17

Prove that the series $\sum_{i = 1}^{\infty} \frac{1}{\sqrt{n}} \sin (\frac{1}{\sqrt{n}})$ is divergent

Francisca Rodden 2022-01-17

Evaluate this integral $\int_{0}^{\frac{π}{4}} \frac{\cos 2 x}{\cos x + \sin x} d x$

petrusrexcs 2022-01-17

A simple equation involving trigonometry
If $\cos θ + \sin θ + \tan θ = \sqrt{2} + 1$
then what is the maximum value of
$\sin θ, \sin^{2} θ$ ?

Kathy Williams 2022-01-17

Integral of $s e c h (x)$

Stefan Hendricks 2022-01-17

How to solve it without integrals:
$\sum_{k = 1}^{n} \sin (\frac{k π}{n}) \sin (\frac{k π}{n^{2}})$

Cheexorgeny 2022-01-16

What is the general solution to the equation $\sin x + \sqrt{3} \cos x = \sqrt{2}$
I need to find the general solution to the equation
$\sin x + \sqrt{3} \cos x = \sqrt{2}$
So I went ahead and divided by 2, thus getting the form
$\cos (x - \frac{π}{6}) = \cos (\frac{π}{4})$
Thus the general solution to this would be
$x = 2 n π \pm \frac{π}{4} + \frac{π}{6}$
Which simplifies out to be,
$x = 2 n π + \frac{5 π}{12}$
$x = 2 n π - \frac{π}{12}$

vegetars8t 2022-01-16

Proving ${(\sin^{2} α + \sin α \cos α)}^{\sin α} {(\cos^{2} α + \sin α \cos α)}^{\cos α} \leq 1$

hadejada7x 2022-01-16

$lim_{x \to 0} \frac{x (1 + a \cos x) - b \sin x}{x^{3}} = 1$ , how to find the constants a,b?

Susan Nall 2022-01-16

$50 \cos^{2} x + 5 \cos x = 6 \sin^{2} x$ , find $\tan x$

PEEWSRIGWETRYqx 2022-01-16

Proving $\frac{1}{{(\tan (\frac{x}{2}) + 1)}^{2} \cos^{2} (\frac{x}{2})} = \frac{1}{1 + \sin x}$

Lucille Davidson 2022-01-16

Maximum and minimum of $f (x) = 2 \sin^{2} x + 2 \cos^{4} x$

zeotropojd 2022-01-16

Is my evaluation of complex trigonometric expression $\sin (\frac{π}{4} + 2 i) - \sin (2 i)$ correct?

abreviatsjw 2022-01-16

Why does $\cot (2 \arctan (A x)) = \frac{1 - {(A x)}^{2}}{2 A x}$

William Curry 2022-01-15

Solving the equation $\sin 5 x = 16 \sin^{5} x$

eiraszero11cu 2022-01-15

Limit $lim_{x \to 0} (\cot x - \frac{1}{\sin x})$

Carol Valentine 2022-01-15

Calculate the limit of $lim_{x \to 1} \frac{1 - x^{2}}{\sin π x}$ only with the fundamental limits

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Trigonometry

Trigonometry Problems - Basics, Advanced & Examples