Precalculus Solutions | Expert Assistance for Problems & Examples

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

Quinn Dean 2022-04-08

Use $e^{i a} + e^{i b}$ to show that $y (t) = 2 A \cos (\frac{δ}{2} t - \frac{ϕ_{1} - ϕ_{2}}{2}) \sin ((ω + \frac{δ}{2}) t + \frac{ϕ_{1} + ϕ_{2}}{2})$
Given formula (1)
$e^{i a} + e^{i b} = 2 e^{i \frac{(a + b)}{2}} \cos (\frac{a - b}{2})$
Formula (1) should be used to show
$y (t) = 2 A \cos (\frac{δ}{2} t - \frac{ϕ_{1} - ϕ_{2}}{2}) \sin ((ω + \frac{δ}{2}) t + \frac{ϕ_{1} + ϕ_{2}}{2})$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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