Solving Trigonometry Equations and Problems with Examples and Tips

$\sin x + \sqrt{3} \cos x = 6 y - y^{2} - 11$

Landen Barber 2022-03-29

$\int_{0}^{2 π} \sqrt{2 - 2 \cos (x)} d x = 2 \int_{0}^{2 π} \sin (\frac{x}{2}) d x$

Arianna Villegas 2022-03-29

How to simplify:
$\frac{4 \sqrt{7}}{3} \cos (\frac{1}{3} \arccos \frac{1}{\sqrt{28}}) + \frac{1}{3}$

Arianna Villegas 2022-03-29

$\frac{1}{4} \tan (\frac{π}{8}) + \frac{1}{8} \tan (\frac{π}{16}) + \frac{1}{16} \tan (\frac{π}{32}) + \dots \dots \infty$
Try:
$\cos x \cdot \cos (\frac{x}{2}) \cdot \cos (\frac{x}{2^{2}}) \dots \dots \cos (\frac{x}{2^{n - 1}}) = \frac{1}{2^{n - 1}} \frac{\cos (x)}{\sin (\frac{x}{2^{n - 1}})}$
Could some help me how to solve ahead

Addison Fuller 2022-03-29

$\cos (\frac{π}{6} \cdot 2 π)$ in radians isn't equal to $\cos (30 \cdot 360)$ in degrees why?
I put $\cos (\frac{π}{6} \cdot 2 π)$ in radians mode on my calculator and i get -0.9890273166 and then I put $\cos (30 \cdot 360)$ in degrees mode and get 1, the answer is the complete opposite of what it should be and in case if you don't know $\frac{π}{6} \cdot 2 π$ converted to degrees equals 30∗360, so I really need an explanation.

ab0utfallingm1z2 2022-03-29

proving that $\sin β \cos (β + θ) = - \sin θ$ implies $\tan θ = - \tan β$

aidinacol7 2022-03-29

Proving $\sin 4 θ = 4 \cos^{3} θ \sin θ - 4 \cos θ \sin^{3} θ$
Using De Moivre's formula:
${(\cos θ + i \sin θ)}^{4} = \cos 4 θ + i \sin 4 θ$

cleffavw8 2022-03-29

Proving $\cos (w_{1} t) + \cos (w_{2} t) = 2 \cos (\frac{1}{2} (w_{1} + w_{2}) t) \cos (\frac{1}{2} (w_{1} - w_{2}) t)$

amonitas3zeb 2022-03-29

Prove: $\frac{\tan x}{1 - \cot x} + \frac{\cot x}{1 - \tan x} = \sec x \csc x + 1$

Tony Mccarthy 2022-03-29

Prove the following trigonometric identity
$\frac{\tan (\frac{π}{4} + x) - \tan (\frac{π}{4} - x)}{\tan (\frac{π}{4} + x) + \tan (\frac{π}{4} - x)} = 2 \sin x \cos x$

Isaac Hampton 2022-03-29

Prove that: $\tan (2 \tan^{- 1} (x)) = 2 \tan (\tan^{- 1} (x) + \tan^{- 1} (x^{3}))$
My Attempt $\tan^{- 1} (x) = A$
$x = \tan (A)$
Now, L.H.S $= \tan (2 \tan^{- 1} (x))$
$= \tan (2 A)$
$= \frac{2 \tan (A)}{1 - \tan^{2} (A)}$
$= \frac{2 x}{1 - x^{2}}$

Jazmyn Holden 2022-03-29

Prove that:
$\tan^{2} 27^{\circ} + 2 {\tan 27}^{\circ} {\tan 36}^{\circ} = 1$

alparcero97oy 2022-03-29

Prove that:
$\sqrt{2} {\sin 10}^{\circ} + \sqrt{3} {\cos 35}^{\circ} = {\sin 55}^{\circ} + 2 {\cos 65}^{\circ}$

limes14514qqmn 2022-03-29

Prove that:
$\frac{\sin^{2} (2 α)}{\sin^{2} (α)} = 4 - 4 \sin^{2} (α)$

blestimd4pz 2022-03-29

prove that $\tan 2 x = \frac{2 \sin x \cos x}{1 - 2 \sin^{2} x}$

Landen Barber 2022-03-29

Prove that $\tan [\frac{π}{4} + \frac{1}{2} \cos^{- 1} (\frac{a}{b})] + \tan [\frac{π}{4} - \frac{1}{2} \cos^{- 1} (\frac{a}{b})] = \frac{2 b}{a}$

aanvarendbq28 2022-03-29

Prove that $\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \leq \frac{1}{8}$

rhedynogh0rp 2022-03-28

development of $\sum_{m = - (M - 1)}^{M - 1} e^{- i m h ξ}$
$\sum_{m = - (M - 1)}^{M - 1} e^{- i m h ξ} = \frac{\sin (M - \frac{1}{2}) h ξ}{\sin \frac{1}{2} h ξ}$
Can you show the process of the development?

mwombenizhjb 2022-03-28

Determine the values of x,y such that $\cos x \cos z \cos y + \sin x \sin y < 0$ for all z

Kason Palmer 2022-03-28

Determine sinus and cosinus : $2 \sin x + 3 \cos x = 3$

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