Trigonometric Equations and Indentities: Real-World Examples

High School
Geometry
Trigonometry
Trigonometric equations and identities

Recent questions in Trigonometric equations and identities

Tiffany Page 2022-11-14

Solving trigonometric equation $\sin (0.001 - t) = \frac{1}{2}$
Thank you for your help.

Aron Heath 2022-11-13

How to find x in some trigonometric equations
How to solve these trigonometric equations?
$\tan 2 x - \sin 4 x = 0$
and
$\tan 2 x = \sin x$
I can't do this, please help me! I did this:
$\begin{aligned} \tan 2 x & = 2 \sin x \\ \frac{\sin 2 x}{\cos 2 x} & = \tan x \end{aligned}$

kaltEvallwsr 2022-11-13

Trigonometric equation; finding all solutions
I'm having a hard time with trigonometric equations. I need to find all solutions to the following equation:
$4 \sin^{2} θ = 3$
Any help will be appreciated.

2022-11-12

If $\cos (x) = \frac{1}{3}$ , and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimal
$\sin (\frac{x}{2}) =$

$\cos (\frac{x}{2}) =$

tan(x/2) =

Jadon Camacho 2022-11-12

Is this trigonometric equation solvable?
The equation is this:
$x \sin (x) = 90 - x$
I've tried to solve it myself, to no avail. After that, I went to a bunch of algebraic equations solvers, which gave me differing results. Is this equation solvable? By solving, I mean finding a definitive numerical answer for the variable x. If it is, then what is the answer (and steps), and if not, why not?

Zackary Diaz 2022-11-11

Help With Solving Trigonometric equations
$(\sin x)^{2} - 5 \sin x \cos x = 0$
What would be the first atep to solve this. I normally get the equation into a quadratic one but I cannot seem to spot the first step here.
What I mean by $(\sin x)^{2}$ incase there will be confusion is "Sin squared x"
Appreciate any help.

Hayley Mcclain 2022-11-11

How can I solve these two simultanious trigonometric equations?? $\sin x \cos y = \frac{1}{4}$ and $3 \tan x = \tan y$
I tried to make it of the form of compound/ allied angles like $\sin (x + y)$ but failed.
Please give me some hint.
Thanks.

Uriah Molina 2022-11-11

Trouble solving a trigonometric equation
I have this problem in the book and no matter how many times I try I cannot isolate θ:
$\begin{matrix} (displayed) & 2 = (θ - 2 c o s θ) (c o s θ) \end{matrix}$

bucstar11n0h 2022-11-11

How could you eliminate y from these equations? $c x - s y = 2$ and $s x + c y = 1$ , where $c = \cos θ$ , $s = \sin θ$

Bayobusalue 2022-11-11

Trigonometric Equations- Tangent
I am able to solve the equation correctly, but I need to use inverse function to find the degree. The actual answer is the following:
$x = \frac{π}{8}, \frac{5 π}{8}, \frac{9 π}{8}, \frac{13 π}{8}$
So I got $\tan x = - 1 + \sqrt{2}$ , and $\tan x = - 1 - \sqrt{2}$ . How can I straight away know which trigonometric identity to use like half angle in the problem?

Siemensueqw 2022-11-11

Trigonometric equation over unit circle
Let us consider the equations
${p_{0}}^{2} + {q_{0}}^{2} = 1 and - a p_{0} \sin s + b q_{0} \cos s = 0$
How do i solve for $p_{0}, q_{0}$ ?

Paula Cameron 2022-11-11

How can the trigonometric equation be proven?
$2 \sin (80 °) = \frac{\sin (60 °)}{\sin (100 °)} \times \frac{\sin (50 °)}{\sin (20 °)}$

Hallie Stanton 2022-11-10

Trigonometric equation inversion
I am trying to invert the following equation to have it with $θ$ as the subject:
$y = \cos θ \sin θ - \cos θ - \sin θ$
I tried both standard trig as well as trying to reformulate it as a differential equation (albeit I might have chosen an awkward substitution). Nothing seems to stick and I keep on ending up with pretty nasty expressions. Any ideas?

Kameron Wang 2022-11-09

Simplify this trigonometric equation (identities)
Please simplify these trigonometric identities and describe step by step (wording).
$\frac{\sec θ - \csc θ}{1 - \cot θ}$

Rosemary Chase 2022-11-09

Trigonometry equation problem
Show that
$\arctan 2 = \arccos (1 / \sqrt{5}) .$
This is the result of solving one trigonometrical equation.

ajakanvao 2022-11-08

Solve a trigonometric equation
I'm trying to solve this trigonometric equation: $3 \tan x + 5 = 2$ . This is how I'm trying to solve it:
$3 \tan x + 5 = 2 \Leftrightarrow \tan x + 5 = \frac{2}{3} \Leftrightarrow x + 5 = 0, 588 + k . π \Leftrightarrow x = - 4, 412 + k . π$
When I check on photomath it tells me I'm correct however in my math book they say the answer is $- \frac{π}{4} + k . π$

figoveck38 2022-11-08

How would I solve this trigonometric equation $\ln [(\sin (x) + \cos (x))^{1 + \sin (2 x)}] = 2$ ?
I know that $1 + \sin (2 x) = (\sin (x) + \cos (x))^{2}$ , but I cant understand which property of logarithms to apply to get the solution here.

Barrett Osborn 2022-11-08

Solve system of 5 trigonometric equations
What is the best way to solve the system of following trigonometric equations with respect to $w_{l}, w_{r}, b_{l}, b_{r}$ ?
$F_{x} = w_{l}^{2} s i n (b_{l}) + w_{r}^{2} s i n (b_{r})$
$F_{z} = w_{l}^{2} c o s (b_{l}) + w_{r}^{2} c o s (b_{r})$
$M_{x} = w_{r}^{2} c o s (b_{r}) - w_{l}^{2} c o s (b_{l})$
$M_{y} = w_{l}^{2} s i n (b_{l}) + w_{r}^{2} s i n (b_{r})$
$M_{z} = w_{r}^{2} s i n (b_{r}) - w_{l}^{2} s i n (b_{l})$
I need to find relation between $w_{l}, w_{r}, b_{l}, b_{r}$ and symbolic coefficients $F_{x}, F_{z}, M_{x}, M_{y}, M_{z}$ .

Nola Aguilar 2022-11-08

Simplify: $(\cos^{4} x - \sin^{4} x) = 2 \sin^{2} x - 1$
But how can anyone show why this is true?
I ended with $\sin^{2} x - \cos^{2} x$

Jefferson Booth 2022-11-07

Why squaring the trigonometric equation changes the solution?
I have a trigonometric equation that is defined as:
$\sin (α) - \cos (α) = \frac{1}{2}$
Solving this equation by mathematica will yield $α = 65.70$ and $α = - 155.705$
But As I solve it analytically, I will obtain different results:
First I exponentiate both sides to the power of two:
$(\sin (α) - \cos (α))^{2} = {\frac{1}{2}}^{2}$
Now I expand the expressions:
$\sin (α)^{2} - 2 \sin (α) \cos (α) + \cos (α)^{2} = \frac{1}{4}$
As $\sin (α)^{2} + \cos (α)^{2} = 1$ , I will have:
$1 - 2 \sin (α) \cos (α) = \frac{1}{4}$
Again if I put $2 \sin (α) \cos (α) = \sin (2 α)$ I will be left with:
$\sin (2 α) = \frac{3}{4}$
Which will readily give $α = 24.3$
So, why I am having different results? I don't understand.

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Trigonometry

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