Solving Trigonometry Equations and Problems with Examples and Tips

Finding number of real solution of $4^{x} - 2^{2 + x} \cos (e^{x}) + 1 = 0$

Elijah Schwartz 2022-04-08

Finding a shift of $f^{- 1} (x)$ , where $f (x) = \sin {x}, x \in [\frac{π}{2}; \frac{3 π}{2}]$

Kale Bright 2022-04-08

Find:
$L = lim_{x \to 0} \frac{\sin (1 - \frac{\sin (x)}{x})}{x^{2}}$

Abbey Ellison 2022-04-08

Find the value of $\tan^{2} \frac{π}{16} + \tan^{2} \frac{2 π}{16} + \tan^{2} \frac{3 π}{16} + \tan^{2} \frac{4 π}{16} + \tan^{2} \frac{5 π}{16} + \tan^{2} \frac{6 π}{16} + \tan^{2} \frac{7 π}{16}$

Joaquin Salas 2022-04-08

Find the value of $9 \tan {10^{\circ}} + 2 \tan {20^{\circ}} + 4 \tan {40^{\circ}} - \tan {80^{\circ}}$

George Michael 2022-04-08

Find the value of
$\sum_{n = 1}^{50} \arctan (\frac{2 n}{n^{4} - n^{2} + 1})$

Frances Simon 2022-04-08

I've been trying to solve this equation for some time now, but have not been able to do it. I know I've been able to solve it before, but I can't remember how.
This is how far I get, but I don't know how to proceed from here. Thank you for your time.
$\arcsin (x) = \arctan (2 x)$
$x = \sin (\arctan (2 x))$
$v = \arctan (2 x)$
$x = \sin (v)$

Markelovnsl 2022-04-08

I'm trying to solve
$\int_{- 1}^{1} x^{2} {(1 - x^{2})}^{\frac{9}{2}} d x$

Devin Dougherty 2022-04-08

I'm looking to simplify
$\sin (2 \cos^{- 1} (\frac{x}{3}))$

Camila Glenn 2022-04-08

I would like to show that
$\sin \frac{π}{3} \sin \frac{2 π}{3} \cdot \sin \frac{3 π}{13} \cdot \dots \cdot \sin \frac{6 π}{13} = \frac{\sqrt{13}}{64}$

poznateqojh 2022-04-08

I would like to show that
$\frac{1}{n π} \int_{- π}^{π} \frac{\sin^{2} (n \frac{x}{2})}{2 \sin^{2} (\frac{x}{2})} d x = 1$

Quinn Moses 2022-04-08

I was evaluating the range of this function in real numbers:
$f (x) = (x + \sqrt{x}) (10 - x + \sqrt{10 - x})$

Santos Mooney 2022-04-08

I search a simplification for
$\arcsin (\frac{1}{\sqrt{2}} \frac{x}{\sqrt{{(x - 1)}^{2} + 1}})$
any idea ? I tried composition, derivation and setting x as a sine, cosine or a tangent in vain.

Deja Vaughn 2022-04-08

How to simplify $B = \cos^{3} ω \sin ω - \sin^{3} ω \cos ω + \frac{\sqrt{3}}{{\sin 20}^{\circ}} - \frac{\sqrt{3}}{{\cos 20}^{\circ}} - 4$ ?

Breanna Mcclure 2022-04-08

How to prove this
$\frac{\sin (A - B) \sin (A - C)}{\sin 2 A} + \frac{\sin (B - C) \sin (B - A)}{\sin (2 B)} + \frac{\sin (C - A) \sin (C - B)}{\sin 2 C} \geq 0$

Aliana Alvarez 2022-04-08

How to prove the following trignometric identity?
$\cot 7 {\frac{1}{2}}^{\circ} = \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}$

Haylee Bowen 2022-04-08

How to prove $2 \sqrt{2 + \sqrt{3}} = \sqrt{2} + \sqrt{6}$

Henry Winters 2022-04-08

How to prove $2 \sin^{2} (80^{\circ}) - \sin (70^{\circ}) = 1$

Marshall Wolf 2022-04-08

How to get the exact value of $\sin (x)$ if $\sin (2 x) = \frac{24}{25}$
I checked various trigonometric identities, but I am unable to derive $\sin (x)$ based on the given information.
For instance: $\sin (2 x) = 2 \sin (x) \cos (x)$

Aiyana Ayers 2022-04-08

Use the power series for $\arctan (x)$ to derive an expression for $π$
Given that the power series for $\arctan x$ is given by
$\sum_{n = 0}^{\infty} {(- 1)}^{n} \frac{x^{2 n + 1}}{2 n + 1}$
for $x \in [- 1, 1]$ how would you show that
$π = 2 \sqrt{3} \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n + 1) 3^{n}} ?$
I've tried by plugging in x=1 to get
$\frac{π}{4} = \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n + 1)}$
but other then plugging in values I have no clue how to reach the conclusion

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