Solving Trigonometry Equations and Problems with Examples and Tips

Prove that $\cos \arctan 1 / 2 = 2 / \sqrt{5}$

Poftethef9t 2022-06-30

Simplify $5 | \sec θ |$ if $θ = \arctan (x / 5)$

Emmy Knox 2022-06-30

Show that $\frac{\tan α + \sqrt{5} \sin α}{2} (\sqrt{5} \cos α - 1)$ is equivalent to $\frac{5}{4} \sin (2 α) - \frac{1}{2} \tan α$
I tried:
$\frac{\frac{\sin α}{\cos α} + \sin α}{2} (\sqrt{5} \cos α - 1) = \frac{\frac{\sin α + \sqrt{5} \sin α \cos α}{\cos α}}{2} (\sqrt{5} \cos α - 1) = \frac{\frac{\sin α}{\cos α} (\sqrt{5} \cos α + 1)}{2} (\sqrt{5} \cos α - 1) = \frac{\tan α (5 \cos^{2} α - 1)}{2} = ? ? ?$

Jaqueline Kirby 2022-06-30

The original question was solve for $θ$ in $65 \cos (2 θ) - 56 \sin (2 θ) - 55 = 0$

Theresa Archer 2022-06-30

How to find the smallest value of $\sin^{4} (α) + \cos^{4} (α)$ ?

Callum Dudley 2022-06-29

Find the Maclaurin series for $\cos^{2} (x)$

Brock Byrd 2022-06-29

I am trying to follow a solution to a problem and it says that ${(\frac{1 + i \tan θ}{1 - i \tan θ})}^{a} = {(\frac{\cos θ + i \sin θ}{\cos θ - i \sin θ})}^{a}$
However, I am unable to see why this would be? It is probably just a simple oversight but I am unsure.

Michelle Mendoza 2022-06-29

Given,
$\cos (β - γ) + \cos (γ - α) + \cos (α - β) = - \frac{3}{2}$
Prove that:
1. $\cos α + \cos β + \cos γ = 0$
2. $\sin α + \sin β + \sin γ = 0$

Holetaug 2022-06-29

Evaluation of $\sum_{n = 1}^{\infty} \arctan (\frac{4 n}{n^{4} - 2 n^{2} + 2})$

Adriana Ayers 2022-06-29

Prove $\sec 2 x + \tan 2 x \equiv \frac{\cos x + \sin x}{\cos x - \sin x}$

Garrett Black 2022-06-29

Prove $\sin 2 x + \sin 4 x + \sin 6 x = 4 \cos x \cos 2 x \sin 3 x$

Leland Morrow 2022-06-29

I need to simplify this expression. I'm not even sure where to start.
$\tan (\arccos (\frac{x}{4}))$

Taniyah Estrada 2022-06-28

What is the Taylor series of
$\sin (5 z) - 5 \sin (z)$
at $z_{0} = π$
I am confused whether to substitute $5 (z - π)$ or $5 z - π$ into the Maclaurin series of $\sin (z)$

Kassandra Ross 2022-06-28

Proving $1 + \tan^{2} 40^{\circ} = \sec^{2} 40^{\circ}$

Winigefx 2022-06-27

Prove that $\sin^{2} \frac{A}{2} \csc 2 A$ , $\sin^{2} \frac{B}{2} \csc 2 B$ , $\sin^{2} \frac{C}{2} \csc 2 C$ are in harmonic progression

flightwingsd2 2022-06-27

Proving whether the series $\frac{\cos (n)}{n}$ is absolutely convergent

minwaardekn 2022-06-27

Trig - Difference formulas to solve $\sqrt{3} \sin θ - \cos θ = 1$

Yahir Crane 2022-06-27

If $2 \tan^{2} x - 5 \sec x - 1 = 0$ has 7 roots in $[0, \frac{n π}{2}]$ then the greatest value of n is?

Kassandra Ross 2022-06-27

Consider $m = \tan x + \frac{\sin x + \cos x}{\sin x - \cos x}$ . Now determine m so that expression has solution .

Emanuel Keith 2022-06-27

Find the leading behavior of $\int_{0}^{\infty} \cos (x (\frac{t^{3}}{3} - t)) d t$

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