Solving Trigonometry Equations and Problems with Examples and Tips

Why $ℑ \frac{1}{1 + e^{- s + i a}} = \frac{\sin (a)}{\cos (a) + \cosh (s)}$ ?

Tristan Meyers 2022-04-10

Whats the integral of
$\tan^{2} (x / 2) d x$

deformere692qr 2022-04-10

Find the maximum and minimum value of $\cos^{2} x - 6 \sin (x) \cos (x) + 3 \sin^{2} x + 2$

linziboobeary1o8p 2022-04-10

If $\sec (θ) + \tan (θ) = \frac{3}{2}$ , then what are the other trig ratios?

Andreas Gallegos 2022-04-09

How do you solve $\frac{2}{3 \sqrt{2}} = \cos (\frac{x}{2})$

Trent Fuller 2022-04-09

How do you simplify the following expression?
$Q = (1 - \tan^{2} (x)) (1 - \tan^{2} (\frac{x}{2})) \dots (1 - \tan^{2} (\frac{x}{2^{n}}))$

Ashleigh Mitchell 2022-04-09

I'm trying to find the value of r where
$\tan^{- 1} \frac{60}{r} = \sin^{- 1} \frac{60}{r - 10}$

Leia Sullivan 2022-04-09

I would like to evaluate
$\int_{π}^{3 \frac{π}{2}} \frac{1}{1 - ϕ \sin 2 θ} d θ$

Jewel Beard 2022-04-09

I want to show that if ABC is a triangle then
$\sin^{2} (\frac{A}{2}) + \sin^{2} (\frac{B}{2}) + \sin^{2} (\frac{C}{2}) = 1 - 2 \sin (\frac{A}{2}) \sin (\frac{B}{2}) \sin (\frac{C}{2})$
Well I eventually got it after much algebra, but I am looking for a shorter solution, or maybe even a geometric one?

Breanna Fisher 2022-04-09

How to show
$\ln (\tan (x) + \sec (x)) = \frac{\ln (1 + \sin x) - \ln (1 - \sin x)}{2}$ is true or false

Albert Byrd 2022-04-09

How to prove
$\tan x + \tan (x + \frac{π}{3}) + \tan (x + \frac{2 π}{3}) = 3 \tan 3 x$

Deangelo Hardy 2022-04-09

Trigonometry equation
$\sin 2 x - \sin 3 x = \sin 7 x - \sin 8 x$

Ean Hughes 2022-04-09

Trigonometric equation:
$2 (\sin^{6} x + \cos^{6} x) - 3 (\sin^{4} x + \cos^{4} x) + 1 = 0$

Tiffany Maldonado 2022-04-09

Trigonometric equations:
$3 \sin B + 4 \cos C = 6$
and
$4 \sin C + 3 \cos B = 1$
show that
$\sin (B + C) = 0.5$

Reagan Gomez 2022-04-09

To prove:
1. $\sum_{k = 1}^{n} \sin (2 k - 1) θ = \frac{\sin^{2} n θ}{\sin θ}$
2. $\sum_{k = 1}^{n} \sin^{2} (2 k - 1) θ = \frac{n}{2} - \frac{\sin 4 n θ}{4 \sin 2 θ}$

Gustavo Lam 2022-04-09

The value of x satisfying the equation $x = \sqrt{2 + \sqrt{2 - \sqrt{2 + x}}}$
(A) $2 \cos 10$
(B) $2 \cos 20$
(C) $2 \cos 40$
(D) $2 \cos 80$

Malik Dean 2022-04-09

The value of $\prod_{{r = 1}}^{10} (1 + {\tan r}^{\circ}) \cdot \prod_{{r = 46}}^{55} (1 + {\cot r}^{\circ})$
Attempt: $\prod_{{r = 1}}^{10} (1 + {\tan r}^{\circ}) = (1 + {\tan 1}^{\circ}) (1 + {\tan 9}^{\circ}) \dots \dots (1 + {\tan 4}^{\circ}) (1 + {\tan 6}^{\circ}) {\tan 5}^{\circ}$ from $\tan (A + B) = {\tan 10}^{\circ} \to \frac{\tan A + \tan B}{1 - \tan A \tan B} = {\tan 10}^{\circ}$
could some help me to solve it

Kennedy Ford 2022-04-09

The Question reads -
$\frac{\cos 5 x + \cos 4 x}{1 - 2 \cos 3 x} = - \cos 2 x - \cos x$

Angela Harrell 2022-04-09

The question given is,
If $x \cos (θ) - \sin (θ) = 1$ then find the value of $x^{2} + (1 + x^{2}) \sin θ$

Jefferson Pacheco 2022-04-08

Finding the range of $f (x) = \cos x (\sin x + \sqrt{\frac{1}{2} + \sin^{2} x})$

The majority of Trigonometry Math problems are quite easy to solve when you have the list of answers that help you see the logic and reasoning. Looking at various examples will help you to see how certain questions are related to provided solutions.

Remember that Trigonometry requires patience and analysis. By following your analysis skills, you will help yourself find the answers. If something remains unclear, start with your exploration of examples again and go step-by-step.

Precalculus

Practice Exercises for Trigonometry