Solving Trigonometry Equations and Problems with Examples and Tips

How do you integrate the following functions:
$\int {(\frac{\cos θ}{1 + \sin^{2} θ})}^{2} d θ$

Corbin Walton 2022-02-26

How to integrate
$\int_{0}^{\frac{π}{2}} \frac{2 a \sin^{2} x}{a^{2} \sin^{2} x + b^{2} \cos x} d x$

Carole Juarez 2022-02-26

Show that
$- 2 \leq \cos θ (\sin θ + \sqrt{\sin^{2} θ + 3}) \leq 2$

Aine Sellers 2022-02-25

I am trying to find this by using integration by parts but I am not sure how to do it.
$\int_{0}^{\frac{π}{2}} {(\sin x)}^{7} {(\cos x)}^{5} d x$

Sarah-Louise Prince 2022-02-25

Prove this equality
$lim_{x \to 0} (\frac{\cos (π x)}{\sin (π x)} - \frac{π x}{\sin^{2} (π x)}) = 0$

Beverley Rahman 2022-02-25

Prove
$\cos (\frac{3 π}{2} + x) \cos (2 π + x) [\cot (\frac{3 π}{2} - x) + \cot (2 π + x) = 1$

Romana Newton 2022-02-25

Can anyone offer please help me solve the following trig identity.
$\frac{1 - \tan (\frac{x}{2})}{1 + \tan (\frac{x}{2})} = \frac{1 - \sin x}{\cos x} = \frac{\cos x}{1 + \sin x}$

Zeenat Horn 2022-02-25

I have to evaluate:
$\int_{0}^{\frac{π}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} d x$

Ayden Case 2022-02-25

Show that:
$\forall n \in N ([{(2 + i)}^{n} + {(2 - i)}^{n}] \in R)$

Fearne Castro 2022-02-25

Find all values for x in the interval $[0^{\circ}, 360^{\circ}]$
$2 \cos x - \cos 2 x = \frac{5}{4}$

Mark Johns 2022-02-25

How can the following function such that no trigonometric functions are present:
$\sin^{3} (\cot^{- 1} (x))$

Vofteldetgpt 2022-02-25

How to evaluate
$\int_{0}^{\frac{π}{2}} 3 \cos^{2} θ d θ$

cooopt392a0i 2022-02-25

Is $\sin^{3} x = \frac{3}{4} \sin x - \frac{1}{4} \sin 3 x$ ?

demonlikw4 2022-02-25

I want to prove that
$2 \arctan \sqrt{x} = \arcsin \frac{x - 1}{x + 1} + \frac{π}{2}$

Rome Frazier 2022-02-25

I recently determined that for all integers a and b such that $a \neq b$ and $b \neq 0$ .
$\arctan (\frac{a}{b}) + \frac{π}{4} = \arctan (\frac{b + a}{b - a})$

Abiha Bellamy 2022-02-25

When is
$\frac{1}{n} \sin (n t) = \frac{1}{n + 2} \sin ((n + 2) t)$ ?

Umaiza Hutton 2022-02-25

Solving an example with imaginary units.
$θ = \arctan (\sqrt{3} + 2)$
$θ = 75^{\circ} = 5 \frac{π}{12}$

oskrnavih92j 2022-02-25

Solve:
$\sin (x - y) = 3 \sin x \cos y - 1$
$\sin (x + y) = - 2 \cos x \sin y$

treetopssan 2022-01-30

Find the roots (real or complex) of the equation $2 a^{2} (1 + \cos x) - {(1 + a^{2} + b^{2})}^{2} = 0, a, b \in R$
ATTEMPT: Solving for x, we arrived with
$x = \arccos [\frac{{(1 + a^{2} + b^{2})}^{2}}{2 a^{2}} - 1]$
However, I got stuck because of the required domain of $\arccos (\cdot)$ which is [-1,1] while the expression $\frac{{(1 + a^{2} + b^{2})}^{2}}{2 a^{2}} - 1$ does not possibly be within this interval for arbitrary values of a and b. Sometimes I am tempted to say that no general solution exists even in C. Can anyone help me out?

segnverd3a 2022-01-30

Evaluating $\frac{1}{\sin (2 x)} + \frac{1}{\sin (4 x)} + \frac{1}{\sin (8 x)} + \frac{1}{\sin (16 x)}$

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