Solving Trigonometry Equations and Problems with Examples and Tips

How to evaluate the limit of this expression?
$lim_{x \to \infty} \frac{\sin^{2} (\sqrt{x + 1} - \sqrt{x})}{1 - \cos^{2} \frac{1}{x}}$

Davian Lawson 2022-04-20

How to evaluate
$\sin^{- 1} (\sqrt{2} \sin θ) + \sin^{- 1} (\sqrt{\cos θ})$

kadetskihykw 2022-04-20

How is
$\frac{\cos \frac{20 π}{3} + i \sin \frac{20 π}{3}}{\cos \frac{15 π}{4} + i \sin \frac{15 π}{4}} = \cos \frac{35 π}{12} + i \sin \frac{35 π}{12}$

nrgiizr0ib6 2022-04-20

We have $△ s A B C$ with the following measures:
$A = 65^{\circ}, B = 75^{\circ}, area = 88 m^{2}$

Sullivan Pearson 2022-04-20

Verifying Trig Equations
$\frac{\tan x}{1 - \cos x} = \csc x (1 + \sec x)$
I have spent a few hours trying to simplify the left side but I can't seem to find the solution. I would appreciate a pointing in the right direction.

Wyatt Flores 2022-04-20

Verifying $\sin 4 θ = 4 \cos^{3} θ \sin θ - 4 \cos θ \sin^{3} θ$

Travis Caldwell 2022-04-20

Verify the identity:
$2 \cos^{4} x - \cos^{2} x - 2 \sin^{2} x \cos^{2} x + \sin^{2} x = \cos^{2} x$

diasenamorn5l 2022-04-20

Verify the identity that I can't get:
$\sec^{2} \frac{x}{2} = \frac{2}{1 + \cos x}$

Ari Sheppard 2022-04-20

Variation of $x \to \tan x$ over $(\frac{π}{2}, π]$ without using derivation?

predorsomwy 2022-04-20

Value of $\frac{\cos 45}{\sec 30 + sc30 s c 30}$

dreangannaa 2022-04-20

Solving a cubic equation involving trigonometric functions
$\sin (x) - \cos (x) = \frac{\sqrt{3}}{2}$
then
$\sin^{3} (x) - \cos^{3} (x) = ?$

komanijuuxw 2022-04-20

Solve identity : $\frac{1 + \sin x \cos x}{\cos^{3} x - \sin^{3} x} + \frac{1}{\sin x + \cos x} + \frac{\sin^{2} x - 2 \cos x - 1}{\cos^{2} x - \sin^{2} x} = \frac{1}{\tan^{2} x - 1}$

acceloq3c 2022-04-20

Solve for x if $\tan^{- 1} {\frac{\sqrt{1 + x^{2}} - 1}{x}} = \frac{π}{45}$

Rowan Huynh 2022-04-20

Solve for $θ$ , find all solutions.
$\csc 3 θ = \sin 3 θ$

broggesy9 2022-04-20

Solve
$\cos x + 8 \sin x - 7 = 0$

Jazmine Sweeney 2022-04-20

Solve
$\tan^{- 1} (\frac{1 - x}{1 + x}) = \frac{1}{2} \tan^{- 1} (x)$

etudiante9c2 2022-04-19

we have the function $f : R^{2} \to R^{2}, f (x) = \cos (x + y)$ .So a function that takes the tuple (x,y) and outputs $\cos (x + y)$ .
Do the formulas like $\cos^{2} (x) + \sin^{2} (x) = 1$ still make sense but in this version ${\cos (x + y)}^{2} + {\sin (x + y)}^{2} = 1$ ?
The formulas made sense with the vision of a trigonometric circle but what happens if there are 2 variables involved?

g2esebyy7 2022-04-19

Value of $\sec^{2} a + 2 \sec^{2} b$
If a,b are 2 real number such that $2 \sin a \sin b + 3 \cos b + 6 \cos a \sin b = 7$ , Then $\sec^{2} a + 2 \sec^{2} b$ is
Try: i am trying to sve it using cauchy schwarz inequality
${[(\sin b) (2 \sin a + 6 \cos a) + (\cos b) (3)]}^{2} \leq (\sin^{2} b + \cos^{2} b) ({(2 \sin a + 6 \cos a)}^{2} + 3^{2})$
Could some help me to solve it

Dylan Yoder 2022-04-19

What is $\tan α$ if $\sin α + \cos α = \frac{\sqrt{3} - 1}{2}$ and $α \in (90^{\circ}, 135^{\circ})$

Porter Mccullough 2022-04-19

The function f is defined, for $x \geq 0$ , by $f (x) = 4 - 3 \cos (\frac{x}{2})$
Given that $f (n a + b) = 2.5$ where a is positive constant and n=0,1,2,..., find the smallest possible value of b and least value of a.

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