Solving Trigonometry Equations and Problems with Examples and Tips

Prove that
$3 {(\sin θ - \cos θ)}^{4} + 6 {(\sin θ + \cos θ)}^{2} + 4 (\sin^{6} θ + \cos^{6} θ) - 13 = 0$

jermandcryspza3 2022-04-02

Prove that
$\frac{1}{\sin^{2} \frac{π}{4 k + 2}} + \frac{1}{\sin^{2} \frac{3 π}{4 k + 1}} + \frac{1}{\sin^{2} \frac{5 π}{4 k + 2}} + \dots + \frac{1}{\sin^{2} \frac{(2 k - 1) π}{4 k + 2}} = 2 k (k + 1)$

Isaac Hampton 2022-04-01

I need help proving the following identity.
$\tan^{2} 10^{\circ} + \tan^{2} 50^{\circ} + \tan^{2} 70^{\circ} = 9$

London Douglas 2022-04-01

I have this equation
$\frac{1 - e^{2}}{1 + e \cos (θ - θ_{0})} = 1 - e \cos η$
and using the identity
$\cos θ = \frac{1 - \tan^{2} \frac{θ}{2}}{1 + \tan^{2} \frac{θ}{2}}$
this becomes
$\sqrt{1 - e} \tan (\frac{θ - θ_{0}}{2}) = \sqrt{1 + e} \tan \frac{η}{2}$
However, I'm unsure about the steps in between.

ikramkeyslo4s 2022-04-01

I have the following function:
$f (x) = \sqrt{3} \cos (x) + \sin (x)$
I am trying to find what the amplitude of this function is without graphing it. I understand the formula for a cosine equation is:
$y = A \cos (B x - C)$

acidizihvzs 2022-04-01

I have
$\frac{\tan 15 °}{1 - \tan {15^{\circ}}^{2}}$

Samara Richard 2022-04-01

Someone can explain me why
$\tan (- \frac{π}{4} + \arctan x) = \frac{x - 1}{x + 1}$

Rex Maxwell 2022-04-01

I am trying to find absolute maximum and absolute minimum values for $f (x) = \cos (x) + \sin (2 x)$ on the interval $[0, \frac{π}{2}]$
I started off by finding the derivative:
$f^{'} (x) = - \sin x + 2 \cos (2 x)$
Then I tried to find the critical numbers. But that's where I ran amuck. I came up with:
$\sin x = 2 \cos (2 x)$
How do I go about solving for x?

ikramkeyslo4s 2022-04-01

I am stuck on this identity
$\frac{2 \sin^{4} x + \cos^{2} x - 2 \cos^{4} x}{3 \sin^{2} x - 1} = 1$

Jaylin Clements 2022-04-01

I am struggling to find the integration of the expression below,
$\int_{- \frac{π}{2}}^{\frac{π}{2}} \cos (a \cos θ) e^{i m θ} e^{- i b \sin θ} d θ$
where a and b are arbitrary constant and m is an integer.

nastupnat0hh 2022-04-01

Solving $x^{2} + y^{2} = 9$ , $\arctan \frac{y + 2}{x + 2} + \arctan \frac{y - 2}{x + 4} = 2 \arctan \frac{y}{x}$ without graphing?

aanvarendbq28 2022-04-01

I am having problems understanding how to write an algebraic expression in x for:
$\sin (\arcsin (x) - \arctan (\frac{2}{x}))$

Rolando Wade 2022-04-01

Solving $2 \sin x (\sqrt{3} \cos x - \sin x) = \sqrt{2} - 1$
I have gone this far:
$4 \sin x \sin (60^{\circ} - x) = \sqrt{2} - 1$

Alfredo Holmes 2022-04-01

Solving $a \sin θ + b \cos θ = c$
I know that the solution is
$θ = \tan^{- 1} \frac{c}{_{- \sqrt{a^{2} + b^{2} - c^{2}}}^{+}} - \tan^{- 1} \frac{a}{b}$

meli199939f 2022-04-01

Solving $e^{\sin x} + e^{\cos x} = e + 1$

blestimd4pz 2022-04-01

Solving $\sin x - \cos x = 1$

Kason Palmer 2022-04-01

How to solve this trigonometric equation: $\sin 3 x + \sin 5 x = \sin 6 x + \sin 2 x$
I tried:
$\sin 3 x + \sin (2 x + 3 x) = \sin (2 \cdot 3 x) + \sin 2 x$
$\sin 3 x + \sin 2 x \cdot \cos 3 x + \cos 2 x \cdot \sin 3 x = 2 \sin 3 x \cdot \cos 3 x + \sin 2 x$

Dexter Odom 2022-04-01

Solving $\cos (\tan^{- 1} x) = \sin (\cot^{- 1} \frac{3}{4})$

nastupnat0hh 2022-04-01

Solving $\cos (π (x - 1)) = 0$

Oliver Tyler 2022-04-01

How to solve limits for trigonometric sequences?
$lim_{n \to \infty} n^{3} (1 - \cos (\frac{1}{n})) \sin (\frac{1}{n})$

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