Trigonometric Equations and Indentities: Real-World Examples

High School
Geometry
Trigonometry
Trigonometric equations and identities

Recent questions in Trigonometric equations and identities

taumulurtulkyoy 2022-10-26

Number of solutions of this trigonometric equation.
Q. Find the number of solutions of the equation $\sin (x) + 2 \sin (2 x) - \sin (3 x) = 3$ , in the interval $x \in (0, π)$
I tried clubbing the $\sin (x)$ and $\sin (3 x)$ terms together but got nothing. I also tried the $\sin (x)$ with $\sin (2 x)$ and $\sin (2 x)$ with $\sin (3 x)$ . How do i do it?

Antwan Perez 2022-10-25

Hard Trigonometric Equation
its possible to solve a equation like
$\prod_{k = 0}^{45} (1 + \tan \frac{k π}{180}) = {[\log_{\frac{\sqrt{6}}{3}} | \sin (2 x) |]}^{\frac{9}{2} \sin (2 x) + 20}$
where I got this equation was wondering which of the intervals contained a solution of it?
1. [0,631|0,747]
2. [0,258|0,395]
3. [0,412|0,627]
4. [0,799|0,814]
5. [0,041|0,107]

Emmy Swanson 2022-10-25

Rewrite $\sin (x + \frac{7 π}{6})$ in terms of sin(x) and cos(x)

Marlene Brooks 2022-10-25

Finding solution of trigonometric equation
How to find the solutions of this trigonometric equation
$\sum_{m = 1}^{6} c o s e c (θ + \frac{(m - 1) π}{4}) c o s e c (θ + \frac{m π}{4}) = 4 \sqrt{2}$
if $0 < θ < π / 2$

Alexander Lewis 2022-10-24

Use trigonometric identities to transform the left side of the equation into the right side $(0 < θ < π / 2)$
$\sin θ \csc θ = 1$

Gerardo Aguilar 2022-10-23

Solving a trigonometric function
How do you solve this trigonometric equation?
Solve the equation for solutions in the interval $[0, 2 π)$
$(\cot (x) - 1) (2 \sin (x) + \sqrt{3}) = 0.$

Pellagra3d 2022-10-23

Trigonometric Equations
Eliminate B from each pair of equations:
$x = \sin B - 3 \cos B and y = \sin B + 2 \cos B$
I've tried solving this simultaneously just as the textbook has guided me through, but it still doesn't work. My initial working out was moving sinB to the left hand side and everything else to the right and solve simultaneously. But that didn't work out, I must have done something wrong, can someone please help me solve this. Thanks!

Tessa Peters 2022-10-22

Sum of roots of trigonometric equation
This is the hardest problem on Georgian (country) high school math exam.
Find all values for parameter a for which the sum of all the roots of the equation:
$\sin (\sqrt{a x - x^{2}}) = 0$
equal to $100$
Note that you can't use calculus and we assume only real roots!

Ryder Ferguson 2022-10-22

Find $d^{2} y / d x^{2}$
$y = x \sin x - 3 \cos x$

racmanovcf 2022-10-13

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value.
$\cos 10^{\circ} \cos 80^{\circ} - \sin 10^{\circ} \sin 80^{\circ}$

mocatgesex 2022-09-30

Find the maximum area of a triangle formed in the first quadrant by the xx-axis, yy-axis and a tangent line to the graph of $f = (x + 6)^{- 2}$

Dana Russo 2022-09-07

$\sqrt{3} \sin x - \cos x = \sqrt{2}$
I think to do :
$\frac{(\sqrt{3} \sin x - \cos x = \sqrt{2})}{\sqrt{2}}$
but i dont get anything. Or to divied by $\sqrt{3}$ :
$\frac{(\sqrt{3} \sin x - \cos x = \sqrt{2})}{\sqrt{3}}$

dripcima24 2022-09-06

I bumped into this question.
$\cos (x) - \sec (x) = 0$
I know it turns into
$\cos^{2} (x) - 1 = 0$
It also equals to
$\sin^{2} (x) = 0$
The answer scheme gave (ans: $0^{\circ}$ , $180^{\circ}$ , $360^{\circ}$ )Why are $90^{\circ}$ , $270^{\circ}$ unacceptable?

Gretchen Allison 2022-09-05

Show that the subset S = {0,2,4,6,8} of Z10 is a subring. Does S have identity?

cyrilicesj 2022-09-05

Complete the identity.
$\sin (x + \frac{3 π}{2}) =$ ?

Ciolan3u 2022-09-05

Solve the identy. $\frac{1 + \sin 2 x}{\cos x + \sin x} = \frac{\cos 2 x}{\cos x - \sin x}$

Damon Cowan 2022-09-04

Prove the following Identity: $\frac{\sin^{2} x - 4 \sin x + 3}{\cos^{2} x} = \frac{3 - \sin x}{1 + \sin x}$

ureq8 2022-09-04

Complete the identity. $\sin^{2} θ / 2 =$ ?

Jimena Hatfield 2022-09-03

Give the exact value of:
a. $\cos (\sin^{- 1} (- .5))$
b. $\cos^{- 1} (\cos 7 π / 6)$

FoomyBiamy5 2022-09-02

Use the opposite angle or periodicity identities to answer.
$\frac{\cos (\frac{3 π}{2}) \sin (6 π)}{\sin (\frac{19 π}{2}) \tan (\frac{21 π}{4})}$

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