Solving Trigonometry Equations and Problems with Examples and Tips

How is it that
$\ln (2 + \tan θ) - \frac{1}{2} \ln (1 + \tan^{2} θ) = \ln (\frac{2 + \tan θ}{\sec θ})$

luminarc24lry 2022-04-21

We all know that $\cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}, \cos (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ and $\cos (\frac{π}{3}) = \frac{1}{2}$ . One can also prove that $\cos (\frac{π}{5}) = \frac{\sqrt{5} + 1}{4}$ . But it seems that $\cos (\frac{π}{7})$ cannot be put in a closed form algebraic expression. Is there a proof of such a claim? I feel like this has to do with the Abel–Ruffini theorem.
The same for $\cos (\frac{π}{8})$ and $\cos (\frac{π}{9})$ . But $\cos (\frac{π}{10}) = \sqrt{\frac{5}{8} + \frac{\sqrt{5}}{8}}$

Dania Robbins 2022-04-21

Verify:
$\sec^{2} x + \tan^{2} x = (1 - \sin^{4} x) \sec^{4} x$

p3sa1bynn 2022-04-21

Value of ${\cos 20}^{\circ} + 2 \sin^{2} 55^{\circ} - \sqrt{2} {\sin 65}^{\circ}$

Davian Lawson 2022-04-21

Value of ${\cos 52}^{\circ} + {\cos 68}^{\circ} + {\cos 172}^{\circ}$ ?

vacinammo288 2022-04-21

Using implicit differentiation, find y' if $\sin (x + y) = y^{2} \cos (x)$

zamenjenot7k 2022-04-21

Using the formula for $\sin (A + B)$ and $\cos (A + B)$ show that:
$\frac{\cos (A - B) - \cos (A + B)}{\sin (A - B) - \sin (A + B)} = \tan (A)$
anybody knows how to get the answer? I keep getting stuck at $\frac{2 \sin (A) \sin (B)}{2 \cos (A) \cos (B)}$

Michael Rivers 2022-04-21

Solve $lim_{x \to \infty} \frac{x + \sin (x)}{2 x + \cos (x)}$

Wissety52 2022-04-21

Solve:
$2 + \cos \frac{3 x}{2} + \sqrt{3} \sin \frac{3 x}{2} = 4 \sin^{2} \frac{x}{4}$

ulcerat9jr 2022-04-21

Solve $\frac{d y}{d x} = \cos (x + y) + \sin (x + y)$
My Attempt
$\frac{d y}{d x} = \sqrt{2} \cos (x + y - \frac{π}{4})$
Set $t = x + y - \frac{π}{4} \Rightarrow y = t - x + \frac{π}{4}$
$\frac{d y}{d x} = \frac{d t}{d x} - 1 = \sqrt{2} \cos t$
$\frac{d t}{d x} = \sqrt{2} \cos (t) + 1$
$\int \frac{d t}{\sqrt{2} \cos (t) + 1} = \int d x$
How do I proceed further to find the general solution ?

Kymani Shepherd 2022-04-21

Solve for x where $0 \leq x \leq 360$
$2 \sin x = \tan x$
I tried this and I ended up with
$\cos x = 2$
Steps: $\sin x = \frac{\tan x}{2}$
$\sin x = \frac{\frac{\sin x}{\cos x}}{2}$
$\sin x = \frac{\cos x}{2} \sin x$
$2 = \cos x$
to find x I did $\cos^{- 1}$ , but $\cos^{- 1} 2$ is a math error

abiejose55d 2022-04-21

Solve for x: $1 + \tan^{2} (x) = 8 \sin^{2} (x), x \in [\frac{π}{6}, \frac{π}{2}]$

kulisamilhh 2022-04-21

Solve
$\sin x + \cos x + \tan x + \csc x + \sec x + \cot x = - 2$
from $0 < x < 2 π$

vacinammo288 2022-04-20

If $0 \leq θ \leq 360$ , and:
$\cos (θ - 35.54) = \frac{8}{\sqrt{74}}$

tobeint39r 2022-04-20

If $\cos^{6} (x) + \sin^{6} (x) = a + b \cos (4 x)$ . Find ab?
As after solving above equation, I get $1 - 3 \sin^{2} (x) \cos^{2} (x) = a + b \cos (4 x)$ . Please help me to solve this problem.

kadetskihykw 2022-04-20

If $\cos (θ) = - \frac{2}{3}$ and $450^{\circ} < θ < 540^{\circ}$ , find
1. The exact value of $\cos (\frac{1}{2} θ)$
2.The exact value of $\tan (2 θ)$

Jazmine Sweeney 2022-04-20

How to find value of this sum?
$\sum_{m = 1}^{\infty} \tan^{- 1} (\frac{2 m}{m^{4} + m^{2} + 2})$

spetterde52g 2022-04-20

If a,b,c are in an Arithmetic Progression (AP), prove that
$\frac{\sin {c} - \sin {a}}{\cos {a} - \cos {c}} = \cot {b}$

Caitlyn Cole 2022-04-20

How to find the integral
$\int_{0}^{70 π} | \cos^{2} x \sin x | d x$

Gage Potter 2022-04-20

How to find : $lim_{x \to \frac{1}{4}} \frac{1 - \tan (π x)}{2 x - \sqrt{x}}$

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