Precalculus Solutions | Expert Assistance for Problems & Examples

I have $\frac{e^{y i} - e^{- y i}}{e^{y i} + e^{- y i}}$ , and I know that this equals
$\frac{\frac{1}{2} (e^{y i} - e^{- y i})}{\frac{1}{2} (e^{y i} + e^{- y i})} = \frac{sinh {y i}}{cosh {y i}} = tanh {y i}$
However, this is also supposed to equal $i \tan y$ . I'm not sure how to get to this result.
I tried doing
$\frac{e^{y i} - e^{- y i}}{e^{y i} + e^{- y i}} = \frac{\frac{e^{2 y i} - 1}{e^{y i}}}{\frac{e^{2 y i} + 1}{e^{y i}}} = \frac{e^{2 y i} - 1}{e^{2 y i} + 1}$

calcolare45pj 2022-03-31

I have no idea how this equation:
${(x^{2} + y^{2} - 1)}^{3} - x^{2} y^{3} = 0$

burubukuamaw 2022-03-31

I have a problem to find answer for this limit.
$lim_{x \to 0} \frac{1 - \cos^{\frac{1}{3}} x}{1 - \cos (x^{\frac{1}{3}})}$

justbethlflql 2022-03-31

Studying convergence of $\int_{a}^{+ \infty} \frac{\sin (x)}{x^{n}}$ for $a, n \in R^{+}$ ?
There is two cases a=0 and $a \neq 0$ . This was my attempt. Case a=0:
$\int_{0}^{+ \infty} \frac{\sin (x)}{x^{n}} = \int_{0}^{1} \frac{\sin (x)}{x^{n}} + \int_{1}^{+ \infty} \frac{\sin (x)}{x^{n}}$
But
$\int_{0}^{1} \frac{\sin (x)}{x^{n}} = \int_{0}^{1} \frac{x}{x^{n}} = \int_{0}^{1} \frac{1}{x^{n - 1}}$
converges for n<2 and diverges for $n \geq 2$ . And
$\int_{1}^{+ \infty} \frac{- 1}{x^{n}} < \int_{1}^{+ \infty} \frac{\sin (x)}{x^{n}} < \int_{1}^{+ \infty} \frac{1}{x^{n}}$
converges for n>1 and diverges for $n \leq 1$ . That means that $\int_{0}^{+ \infty} \frac{\sin (x)}{x^{n}}$ converges for $n \in [1, 2]$ and diverges for $n \in R - [1, 2]$ .

xxgetthisar08 2022-03-31

I cannot find the one-sided limit
$lim_{x \to \frac{π}{2} + 0} \frac{\sqrt{1 + \cos 2 x}}{\sqrt{π} - \sqrt{2 x}}$

abitinomaq1 2022-03-31

I can't find a way to solve this:
$\int_{\frac{π}{2}}^{π} \sqrt{8 \sin^{2} (t) \cos^{2} (t)} d t$

ezpimpin6988ok1n 2022-03-31

Solving the system: $11 {\cos x}_{1} + 12 {\cos x}_{2} = 0$ and $11 {\sin x}_{1} + 12 {\sin x}_{2} = 17$

Pablo Dennis 2022-03-31

Solving this trigonometric equation:
$\sqrt{3} \cos x - 3 \sin x = 4 \sin 2 x \cos 3 x$

Oliver Carson 2022-03-31

Solving the equation $\tan {x} + \tan \frac{x}{4} = 2$
1st attempt: I use the following identity $\tan 2 x = \frac{2 \tan x}{1 - \tan^{2} x}$ . Then get the following equation
$u^{5} - 2 u^{4} - 8 u^{3} + 12 u^{2} + 3 u + 2 = 0$
where $u = \tan \frac{x}{4}$ . But i can't find any root for this equation.
2nd attempt:
$\tan {4 x} + \tan x = 2 \to \sin {4 x} \cos {x} + \sin {x} \cos {4 x} = 2 \cos {4 x} \cos {x} \to \sin {5 x} = 2 \cos {4 x} \cos {x}$
$\sin {5 x} = 2 \cos {4 x} \cos {x} \to \frac{1}{2} \sin {5 x} = \cos {4 x} \cos {x} \to \cos ({2 k π \pm \frac{π}{3}}) \sin {5 x} = \cos {4 x} \cos {x}$
I can't continue from here.

alparcero97oy 2022-03-31

I am trying to completely simplify the derivative of the following function:
$f (x) = \sqrt{16 - x^{2}} - 4 \cos^{- 1} (\frac{x}{4})$

acidizihvzs 2022-03-31

How would you evaluate the integral
$\int_{0}^{π} (\frac{π}{2} - x) \sin (\frac{3 x}{2}) \csc (\frac{x}{2}) d x$

Anahi Solomon 2022-03-31

How would you solve:
$2 \csc^{2} x = 3 \cot^{2} x - 1$

metalskaashw 2022-03-31

Solving $\tan (x + 1) - \tan (x) = 0$

Zoie Phillips 2022-03-31

How to solve the equation
$\tan^{2} (2 x) + 2 \tan (2 x) \cdot \tan (3 x) - 1 = 0$

Nathen Peterson 2022-03-31

How to solve the equation
$\cos^{2} (x) + \cos^{2} (2 x) + \cos^{2} (3 x) = 1$

ikramkeyslo4s 2022-03-31

$4 {\sin 72}^{\circ} {\sin 36}^{\circ} = \sqrt{5}$

Coradossi7xod 2022-03-31

$3 p \sin x - (p + \sin x) (p^{2} - p \sin x + \sin^{2} x) = 1$ has a solution for x. Then number of integral solutions of p are ?

metalskaashw 2022-03-31

Solving for $α$
$\tan α + 2 \tan 2 α + 4 \tan 4 α + 8 \tan 8 α + 16 \tan α = \cot α$

ropowiec2gkc 2022-03-31

$\sin (\frac{x}{2}) + \cos (x) = 0$ , Solve for x of $0^{\circ} \leq x < 360^{\circ}$

Zack Mora 2022-03-31

$\sum_{k = 1}^{10} (\sin \frac{2 π k}{11} - i \cos \frac{2 π k}{11}) =$ ?

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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