Solving Trigonometry Equations and Problems with Examples and Tips

If $\tan (20^{\circ}) = p$ , find $\frac{\tan (160^{\circ}) - \tan (110^{\circ})}{1 + \tan (160^{\circ}) \tan (110^{\circ})}$

dooporpplauttssg 2022-04-22

If $\tan (\frac{α}{2}) = m$ , then evaluate $\frac{1 - 2 \sin^{2} (\frac{α}{2})}{1 + \sin α}$
How to evaluate this?

Abbigail Robles 2022-04-22

If $\cos 3 A + \cos 3 B + \cos 3 C = 1$ in a triangle, find one of its length

Terrence Moore 2022-04-22

If $\frac{\cos (α - 3 θ)}{\cos^{3} θ} = \frac{\sin (α - 3 θ)}{\sin^{3} θ} = m$ prove that $\cos α = \frac{2 - m^{2}}{m}$

Naomi Hopkins 2022-04-22

If $\sin {x} = t, x \in (\frac{3 π}{2}, 2 π)$ , what is $\tan x$ ?
So, according to the interval in which x lies, the value of the sine is negative, and positive for the cosine. Using trig identity I get that
$\cos {x} = \pm \sqrt{1 - \sin^{2} {x}} = \pm \sqrt{1 - t^{2}}$
Knowing the signs of sine and cosine, I pick $\sqrt{1 - t^{2}}$ . Computing tanx I get
$\tan {x} = \frac{\sin {x}}{\cos {x}} = \frac{\sin {x}}{\sqrt{1 - \sin^{2} {x}}} = \frac{t}{\sqrt{1 - t^{2}}}$

Halle Marsh 2022-04-22

If $\tan (α) = 2 - \sqrt{3}$ , find the value of the acute angle $α$

Ezequiel Olson 2022-04-22

If $(1 + \cos A) (1 + \cos B) (1 + \cos C) = (1 - \cos A) (1 - \cos B) (1 - \cos C)$
then prove that each side
$= \pm \sin A \sin B \sin C$

compyac 2022-04-22

How to find the maximum value of $12 \sin x - 9 \sin^{2} x$

Sydney Stanley 2022-04-22

How to evaluate
$\int \frac{\sin^{3} x}{\cos^{5} x} d x$

Ellie Castro 2022-04-22

We are asked to find the range of the function
$f (x) = \frac{\sin x - 1}{\sqrt{3 - 2 \cos x - 2 \sin x}}, for 0 \leq x \leq 2 π$

Judith Warner 2022-04-22

Solve $\sin (x) - \sin (\frac{π}{3} - x) = \sqrt{\frac{3}{2}}$

tefoldaavv 2022-04-22

Solve:
$P = \prod_{k = 1}^{45} \csc^{2} {(2 k - 1)}^{\circ} = m^{n}$

occhei042 2022-04-22

Solve for x: $\arctan 2 x + \arctan 3 x = (\frac{π}{4})$
$\arctan (\frac{2 x + 3 x}{1 - 2 x \cdot 3 x}) = \frac{π}{4}$
$\frac{5 x}{1 - 6 x^{2}} = \tan \frac{π}{4} = 1$
$6 x^{2} + 5 x - 1 = 0$
$(6 x - 1) (x + 1) = 0$
$x = - 1, \frac{1}{6}$
The answer however rejects the solution x=-1 saying that it makes the L.H.S of the equation negative. I don't understand this, I don't see how x=-1 makes the L.H.S. negative.

compyac 2022-04-22

Solve
$2 \sin^{3} x + \sin 3 x + 3 \sin^{2} x \cos x + \cos^{3} x = 0$

yopopolin10d 2022-04-22

Solve
$\cos x < \frac{\sqrt{3}}{2}, x \in [0, 2 π]$

Caitlyn Cole 2022-04-22

Solve
$- \sin^{2} θ + 2 \cos θ + \cos^{2} θ = 0$
Using the quadratic formula.
This is what you should get
$θ = \cos^{- 1} (\frac{- 1 + \sqrt{3}}{2})$

Dereon Guzman 2022-04-21

Please help me to prove this trigonometric equation.
$\cos (36^{\circ}) - \cos (72^{\circ}) = \frac{1}{2}$

albusgks 2022-04-21

Need to find a $3 \cot (x + y)$ if $\tan (x)$ and $\tan (y)$ are the solutions of $x^{2} - 3 \sqrt{5} x + 2 = 0$

sexe4yo 2022-04-21

My task is to evaluate
$\sin (- \frac{π}{6} + \frac{1}{2} \arccos (\frac{1}{3}))$

misangela4gi 2022-04-21

Is a following function periodic $f (x) = \tan x + \tan (\sqrt{2} x)$

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