Solving Trigonometry Equations and Problems with Examples and Tips

If $| \sin^{2} x + 17 - x^{2} | = | 16 - x^{2} | + 2 \sin^{2} x + \cos^{2} x$ then x lies in what interval?

Eileen Garza 2022-04-23

If $\frac{\cos^{4} α}{x} + \frac{\sin^{4} α}{y} = \frac{1}{x + y}$ , prove that $\frac{d y}{d x} = \tan^{2} α$

Porter Mccullough 2022-04-23

If $α + β = \frac{π}{4}$ , then simplify $(\tan α + 1) (\tan β + 1)$

hadaasyj 2022-04-23

How to find a solution for $\sin (θ) - \sqrt{\sin (θ) + \cos (θ)} - \cos^{2} (θ) = 0$ where $θ$ in $[0, 2 π]$

hapantad2j 2022-04-23

How to evaluate $\int \frac{1 + \cos 2 x}{\sin^{2} 2 x}$

abiejose55d 2022-04-23

How to evaluate
${(\cos \frac{5 π}{9})}^{11} + {(\cos \frac{7 π}{9})}^{11} + {(\cos \frac{11 π}{9})}^{11}$

estrigaslju 2022-04-23

How to calculate $\int \frac{x^{3}}{\sqrt{9 - x^{2}}}$

estroishave4 2022-04-23

How to compute
$S = \csc^{2} \frac{π}{14} + \csc^{2} \frac{3 π}{14} + \csc^{2} \frac{5 π}{14}$

Angeline Hayden 2022-04-23

How prove that sum
$\frac{1}{\sin^{2} \frac{π}{2 n}} + \frac{1}{\sin^{2} \frac{2 π}{2 n}} + \dots + \frac{1}{\sin^{2} \frac{(n - 1) π}{2 n}} = \frac{2}{3} (n - 1) (n + 1)$

ngihlungeqtr 2022-04-23

How is this transition possible:
$e^{u} = \tan (\frac{π}{4} + \frac{θ}{2}) given$
${\frac{e^{\frac{u}{2}}}{e^{- \frac{u}{2}}}} = \frac{1 + \tan (\frac{θ}{2})}{1 - \tan (\frac{θ}{2})}$

Elise Winters 2022-04-22

On the roots of
$t^{4} - 6 \sqrt{3} t^{3} + 8 t^{2} + 2 \sqrt{3} t - 1 = 0$

Sydney Stanley 2022-04-22

Number of solutions of $3 \sin^{2} x + \cos^{2} x + \sqrt{3} \sin x + \cos x + 1 = \sqrt{3} \sin x \cos x$ in $[0 10 π]$
My Try:
The given equation is
$2 + 2 \sin^{2} x + 2 \sin (x + \frac{π}{6}) = \frac{\sqrt{3}}{2} \sin (2 x)$
$\Rightarrow$
$3 + 2 \sin (x + \frac{π}{6}) = \frac{\sqrt{3}}{2} \sin (2 x) + \cos (2 x)$

Travis Caldwell 2022-04-22

Is it possible to expand
$\sin (2 x + 1) \cdot \sin (2 x + 1)$ ?

redupticslaz 2022-04-22

Implict differentiation:
$x \cos (4 x + 3 y) = y \sin x$

bacfrancaiso0j 2022-04-22

If $a \sin^{2} x + b \cos^{2} x = c$
$b \sin^{2} y + a \cos^{2} y = d$
$a \tan x = b \tan y$
then prove that
$\frac{a^{2}}{b^{2}} = \frac{(d - a) (c - a)}{(b - c) (b - d)}$

Jakayla Benton 2022-04-22

If $4 \cos^{2} (\frac{k π}{j})$ is the greatest root of the equation
$x^{3} - 7 x^{2} + 14 x - 7 = 0$
where $gcd (k, j) = 1$
Evaluate $k + j$

Essence Byrd 2022-04-22

Simplify $\arcsin (\cos (2 x)), 0 \leq x \leq (\frac{π}{2})$
I used the identity $\sin ((\frac{π}{2}) - x) = \cos x$ and I got $(\frac{π}{2}) - 2 x$

Jazmine Sweeney 2022-04-22

If $\sin^{8} (x) + \cos^{8} (x) = \frac{48}{128}$ then find the value of x?

Averie Ray 2022-04-22

If $\tan x - \sin x = a$ , what is $\sec^{3} (x) - 1$ in terms of a

occhei042 2022-04-22

How to calculate $\frac{I_{n + 2}}{I_{n}}$ of $I_{n} = \int_{\frac{- π}{2}}^{\frac{π}{2}} \cos^{n} θ d θ$
I could calculate that $n I_{n} = 2 \cos^{n - 1} θ \sin θ + 2 (n - 1) \int_{0}^{\frac{π}{2}} I_{n - 2} d θ$ but how do I caluclate the $I_{n + 2}$ ?

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