Precalculus Solutions | Expert Assistance for Problems & Examples

How do you simplify $- 3 i (2 - 5 i) - (7 + i) ?$

Turnseeuw 2022-01-31

How do you multiply $(1 + i) (1 - i) ?$

Selena Cowan 2022-01-31

How do you multiply $(4 + 2 i) (3 - i)$ ?

Madilyn Fitzgerald 2022-01-31

How do you simplify $(1 + 5 i) (1 - 5 i) ?$

Jay Mckay 2022-01-31

How do you simplify $- \sqrt{- 9} \cdot \sqrt{4}$ ?

Gavin Frye 2022-01-31

How do you simplify $(\frac{1}{2} + \frac{2}{5 i}) + (\frac{1}{20} - \frac{1}{5 i})$ ?

mairie0708zl 2022-01-30

How to solve $\cos (θ + ∠)$ equation?
I cant

Gerald Ritter 2022-01-30

Evaluating $lim_{x \to 0} \frac{\cos x - \cos 3 x}{\sin 3 x^{2} - {\sin x}^{2}}$
Is there a simple way of finding the limit?
I know the long one: rewrite it as
$- lim_{x \to 0} \frac{\cos x - \cos (3 x)}{\sin (3 x^{2})} \cdot \frac{1}{1 - \frac{\sin (3 x^{2})}{\sin (x^{2})}}$
and then find both limits in separately applying LHospitals rule several times. The answer is 2

Marissa English 2022-01-30

Consider the series
$\sum_{n = 1}^{\infty} \log (1 + \frac{1}{| \sin (n) |})$
Determine whether it converges absolutely or conditionally.
I am trying to apply Cauchy condensation test, but I am not sure whether the given series is non-increasing or not.

derlingasmh 2022-01-30

Proving identity $\cos^{2} a = {sinh}^{2} b$ if $\sin (a + i b) = \cos b + i \sin b$

treetopssan 2022-01-30

Find the roots (real or complex) of the equation $2 a^{2} (1 + \cos x) - {(1 + a^{2} + b^{2})}^{2} = 0, a, b \in R$
ATTEMPT: Solving for x, we arrived with
$x = \arccos [\frac{{(1 + a^{2} + b^{2})}^{2}}{2 a^{2}} - 1]$
However, I got stuck because of the required domain of $\arccos (\cdot)$ which is [-1,1] while the expression $\frac{{(1 + a^{2} + b^{2})}^{2}}{2 a^{2}} - 1$ does not possibly be within this interval for arbitrary values of a and b. Sometimes I am tempted to say that no general solution exists even in C. Can anyone help me out?

Haialarmz6 2022-01-30

Solve $8 \sin x = \frac{\sqrt{3}}{\cos x} + \frac{1}{\sin x}$
My approach is as follow
$8 \sin x - \frac{1}{\sin x} = \frac{\sqrt{3}}{\cos x}$
On squaring we get
$64 \sin^{2} x + \frac{1}{\sin^{2} x} - 16 = \frac{3}{\cos^{2} x}$
$(64 \sin^{4} x - 16 \sin^{2} x + 1) (1 - \sin^{2} x) = 3 \sin^{2} x$
Solving and re-arranging we get $- 64 \sin^{6} x + 80 \sin^{4} x - 20 \sin^{2} x + 1 = 0$
Using the substitution $\sin^{2} x = t$
$- 64 t^{3} + 80 t^{2} - 20 t + 1 = 0$
I am not able to solve it from hence forth

jelentetvq 2022-01-30

Solve the equation $\frac{\sqrt{3}}{2} \sin (x) - \cos x = \cos^{2} x$
My approach $\cos^{2} x = 1 - \sin^{2} x$
$\frac{\sqrt{3}}{2} \sin x - \cos^{2} x = \cos x$
$\frac{\sqrt{3}}{2} \sin x + \sin^{2} x - 1 = \cos x$
$\sqrt{3} \sin x + 2 \sin^{2} x - 2 = 2 \cos x$
Though the equation comes in form of $\sin x$ from here onward after squaring still not getting the answer.

bistandsq 2022-01-30

Find the general solution (i) $\cot θ = - d \frac{1}{\sqrt{3}}$
(ii) $4 \cos^{2} θ = 1$

Willow Carrillo 2022-01-30

Find $λ$ such that f(x) has no point of local maxima or minima in $| x | < \frac{π}{2}$
Let
$f (x) = {(\sin (x))}^{3} + λ {(\sin (x))}^{2}$
for every x in domain of $(\frac{- π}{2}, \frac{π}{2})$ has no point of local maxima or minima, then find the value of $λ$ for the given condition to follow.
1): found f′(x) and equated with zero to find that it only matters by $(3 \sin x + 2 λ)$ and sinx to have change in the sign of derivative around zero.So the $λ$ becomes 0 and 0 becomes the point of inflection.

treetopssan 2022-01-30

Let $z = 2 e^{10 π \frac{i}{21}} and w = e^{π \frac{i}{7}}$ . Then if $[{(z - w)}^{6} = r e^{i θ}]$ where $r \geq 0$ and $0 \leq θ \leq 2 π$ what is the ordered pair $(r, θ)$ ?

plorinosakl 2022-01-30

Is $\sin 2 x \geq 0$ same as $\sin x \cos x \geq 0$ ?

Madilyn Fitzgerald 2022-01-30

Given $\sin x = \frac{3}{4}$ and $\frac{π}{2} < x < π$ , find $\sin (x + \frac{π}{6})$
I have been trying to calculate this question
$\sin θ = \frac{3}{4}$
$\frac{π}{2} < θ < π$
$\sin (θ + \frac{π}{6}) = \sin θ . \frac{\cos π}{6} + \cos θ . \frac{\sin π}{6}$
$= \frac{3}{4} . \frac{\sqrt{3}}{2} + \cos θ \frac{.1}{2}$
$= \frac{3 . \sqrt{3} + 4 \cos θ}{8}$
The answer is: $\frac{3 . \sqrt{3} - \sqrt{7}}{8}$
However I do not know how to get to it.

Clare Baldwin 2022-01-30

Equation of line passing through (1,2) and perpendicular to the line 2x+3y=1.
i have attempted so far
to find a slope of line
2x+3y=1
Slope m of a line of the form Ax+By=C equals $- \frac{A}{B}, A = 2, B = 3$
$m = - \frac{23}{}$
the point slope formula
$y - y_{1} = m (x - x_{1})$
the point given (1,2)
$y - 2 = - \frac{23}{x - 1}$
$y = - \frac{23}{x} + \frac{23}{+} \frac{21}{\times} \frac{33}{}$
$y = - \frac{23}{x} + \frac{23}{+} \frac{63}{}$
$y = \frac{23}{x} + \frac{83}{}$
is this right answer ?

segnverd3a 2022-01-30

Evaluating $\frac{1}{\sin (2 x)} + \frac{1}{\sin (4 x)} + \frac{1}{\sin (8 x)} + \frac{1}{\sin (16 x)}$

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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