Trigonometric Equations and Indentities: Real-World Examples

High School
Geometry
Trigonometry
Trigonometric equations and identities

Recent questions in Trigonometric equations and identities

Alisha Pitts 2022-01-24

Using De Moivre's law to compute ${(- \sqrt{3} + i)}^{\frac{2}{3}}$
Question:
If $z = - \sqrt{3} + i$ , then $z^{\frac{2}{3}} = ?$

Miguel Davenport 2022-01-24

If a,b,c are positives such that $a + b + c = \frac{π}{2}$ and $\cot (a), \cot (b), \cot (c)$ is in arithmetic progression, find $\cot (a) \cot (c)$

maliaseth0 2022-01-24

Solving $\sin (\arcsin (a - x) - c) = \sin$ for x $(\arcsin (b + x) + π - c) + d$

Swebaceacichegh 2022-01-24

I am practice about find the x as solution of
$\sin (\frac{2 x}{3} + 36^{\circ}) = \frac{12}{}$
Between $0^{\circ} and 360^{\circ}$ Here is my work so far,
$\sin (\frac{2 x}{3} + 36^{\circ}) = {\sin 30}^{\circ}$
I try using arcsin
$\frac{2 x}{3} + 36^{\circ} = 30^{\circ}$
$\frac{2 x}{3} = - 6^{\circ}$
$x = - 9^{\circ}$
I am stucked here.

Alex Cervantes 2022-01-24

Prove that $\cos e c^{2} A \cdot \sec^{2} A = \tan^{2} A + \cot^{2} A + 2$

Lainey Goodwin 2022-01-23

How to prove the identity $\sin 2 x + \sin 2 y = 2 \sin (x + y) \cos (x - y)$

Sereinserenormg 2022-01-23

The range of $f (x) = \cos^{2 n} (x) + \sin^{2 n} (x)$
I have $f (x) = \cos^{2 n} (x) + \sin^{2 n} (x), n \in N, n \geq 2, x \in R$ I need to find the range of the function. I took n=2 and I got $f (x) = 1 - {\frac{12}{\sin}}^{2} (2 x)$ and the range of this is [1/2,1]
Also, for n=3 I got [1/4,1].
How to find the range for n?

Jamya Elliott 2022-01-23

Solving $4 \sin^{4} x - 4 \sin^{2} x + 1 = 0, x \in [0, 2 π ⟩$
I am having problem solving this trig equation. Every time I try to simplify or substitute sinx with u, I get $x = \emptyset$ .
How do I go about solving this equation?
$4 \sin^{4} x - 4 \sin^{2} x + 1 = 0, x \in [0, 2 π ⟩$

Jamarion Kerr 2022-01-23

Solve the trigonometry equation in rational form.
$\frac{\tan^{2} x \sin^{2} x}{1 - \sin^{2} x \cos 2 x} + \frac{\cot^{2} x \cos^{2} x}{1 - \cos^{2} x \cos 2 x} + \frac{2 \sin^{2} x}{\tan^{2} x + \cot^{2} x} = \frac{32}{}$
What I thought:
$\frac{\tan^{2} x \sin^{2} x}{1 - \sin^{2} x \cos 2 x} + \frac{\cot^{2} x \cos^{2} x}{1 - \cos^{2} x \cos 2 x} + \frac{2 \sin^{2} x}{\tan^{2} x + \cot^{2} x} - \frac{32}{=} 0$
Transform each fraction into $\tan x$ , then you can factor out ${(\tan x - 1)}^{2} {(\tan x + 1)}^{2}$

Kendall Holder 2022-01-23

P(t) models the distance of a swinging pendulum (In CM) from the place it has travelled t seconds after it starts to swing. Here, t is entered in radians.
$P (t) = - 5 \cos (2 π t) + 5$
What is the first time the pendulum reaches 3.5 CM from the place it was released?
Round your final answer to the hundredth of a second.
Ok, so I did this to get the solution:
$3.5 = - 5 \cos (2 π t) + 5$
$- 1.5 = - 5 \cos (2 π t)$
$0.3 = \cos (2 π t)$
$\cos - 1 (0.3) = 2 π t$
$\frac{\cos^{- 1} (0.3)}{2 π} = t$
The fact is this gives me 11.55 seconds to get to 3.5 CM, which does not sound right. Where did I go wrong and how can I fix it?

Stefan Hendricks 2022-01-17

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

Francisca Rodden 2022-01-17

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

Ernest Ryland 2022-01-17

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

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 $s e c h (x)$

vegetars8t 2022-01-16

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

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,
$x = 2 n π + \frac{5 π}{12}$
$x = 2 n π - \frac{π}{12}$

PEEWSRIGWETRYqx 2022-01-16

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

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

The majority of students do not like Trigonometry because they find all the questions and equations overly complex. Do not let it frighten you because we have lots of answers that will help you achieve solutions by turning to already existing tasks. We have practical works on all the twelve trigonometric identities and equations with 45 formulas that you can apply in your work. Since you can take a look at the resolved assignments, you will become a trigonometric identities and equations solver that can start with the formulas and continue with the graphics, analytical calculation, and related word problems.

Trigonometry

Demystify Trigonometric Equations and Identities with Step-by-Step Examples and Expert Guidance