Solving Trigonometry Equations and Problems with Examples and Tips

Prove that $\cos (π / 7)$ is root of equation $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$

Aiden Barry 2022-05-22

Find the minimum value of the following expression
$\frac{\sin α \sin β}{\sin^{2} \frac{γ}{2}} + \frac{\sin β \sin γ}{\sin^{2} \frac{α}{2}} + \frac{\sin γ \sin α}{\sin^{2} \frac{β}{2}},$
where $α, β$ and $γ -$ − angles of some triangle?

Simone Werner 2022-05-22

Simplify $\frac{1 - \cos^{2} (- θ)}{1 + \tan^{2} (- θ)}$

Brice Colon 2022-05-22

Complex number in cosine: $\cos (\log (i^{4 i}))$

codosse2e 2022-05-22

How to put $\frac{1}{\cos θ - j \sin θ}$ in the form a+jb? ( $j^{2} = - 1$ )

reryfaikear 2022-05-21

Convergence of $\sum_{k \geq 1} e^{- t k} \cos k z$

Landon Bonilla 2022-05-21

$(\cos 2 x + \cos x - 1) / (\cos 2 x) > 2$ for $x \in< 0, π >$

Laurel Yoder 2022-05-21

Prove: $\tan \frac{π}{24} = 2 \sqrt{2 + \sqrt{3}} - \sqrt{3} - 2$

brendijadq 2022-05-21

If real numbers x and y fit the equality $\frac{2 x + i}{y + i} = \frac{1 + i \sin α}{1 + i \sin 3 α}$ , what does $\frac{x}{y}$ equal?

Ashly Harrell 2022-05-21

Prove that: $\sec^{2} 20^{\circ} + \sec^{2} 40^{\circ} + \sec^{2} 80^{\circ} = 36$

Monfredo0n 2022-05-21

Solve $\cos (z) + \sin (z) = 2$
My work:
$\begin{aligned} \cos (z) + \sin (z) = 2 & ⟹ e^{i z} & + e^{- i z} + e^{- i z} - e^{i z} = 4 \\ ⟹ e^{- i z} & = 2 \\ ⟹ e^{- i z} & = e^{\ln (2) + 2 π n i} \\ ⟹ - i z & = \ln (2) + 2 π n i \\ ⟹ z & = i \ln (2) - 2 π n \end{aligned}$
but apparently the answer is $z = \frac{π}{4} + 2 n π \pm i \ln (\sqrt{2} + 1)$

Wayne Steele 2022-05-21

Grade 12 trigonometric identities: $\frac{\cos 2 x}{1 + \sin 2 x} = \tan (\frac{π}{4} - x)$

Avah Knapp 2022-05-21

Given $\cos x = 12 / 13$ ,where $0 < x < 90^{\circ}$ , find the value of $\sin (2 x)$

Brice Colon 2022-05-21

Solving $\csc (x) + \cot (x) = p$

Carlie Fernandez 2022-05-21

inverse laplace transform of $\frac{s^{3}}{(s^{2} + 4)^{2}}$

Hayley Sanders 2022-05-21

Expand $(\tan x - \sqrt{3}) (3 \tan x + \sqrt{3})$

Jaycee Mathis 2022-05-21

How to find $\sin (- \frac{11 π}{12})$

Avah Knapp 2022-05-21

Establish the identity:
$\frac{\cot θ + \sec θ}{\cos θ + \tan θ} = \sec θ \cot θ$

infogus88 2022-05-21

Prove that $\cos^{6} β - \sin^{6} β = \frac{1}{16} (15 \cos 2 β + \cos 6 β)$

Thomas Hubbard 2022-05-21

Prove that:
$\cos^{2} θ \sin^{4} θ = \frac{1}{32} (\cos 6 θ - \cos 2 θ + 2 - 2 \cos 4 θ)$

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