Precalculus Solutions | Expert Assistance for Problems & Examples

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.

ikramkeyslo4s 2022-04-01

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

Rowan Callahan 2022-04-01

I am trying to factor the following polynomial:
$8 x^{3} - 4 x^{2} y - 18 x y^{2} + 9 y^{3}$

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:
$\sin (\arcsin (x) - \arctan (\frac{2}{x}))$

meli199939f 2022-04-01

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

Alfredo Holmes 2022-04-01

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

Rolando Wade 2022-04-01

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

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:
$\sin 3 x + \sin (2 x + 3 x) = \sin (2 \cdot 3 x) + \sin 2 x$
$\sin 3 x + \sin 2 x \cdot \cos 3 x + \cos 2 x \cdot \sin 3 x = 2 \sin 3 x \cdot \cos 3 x + \sin 2 x$

nastupnat0hh 2022-04-01

Solving $\cos (π (x - 1)) = 0$

Dexter Odom 2022-04-01

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

Oliver Tyler 2022-04-01

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

atenienseec1p 2022-04-01

How to solve
$3 \sin^{2} x - 5 \sin x \cos x + 2 \cos^{2} x = 0$

Dexter Odom 2022-04-01

Range of $y = \cot^{- 1} x \cot^{- 1} (- x)$
Attempt: Let $\cot^{- 1} x = θ$ . Then $y = θ (π - θ)$ ;since $θ \in (0, π)$ .Then $θ^{2} - π θ + y = 0$ .For $θ$ to be real, $y \leq \frac{π^{2}}{4}$
Thus $0 < y \leq \frac{π^{2}}{4}$

Dumaen80p3 2022-04-01

Question: Realise the denominator $\frac{3 + 2 i \sin θ}{1 - 2 i \sin θ}$ and hence find θ if the expression is purely imaginary.
I've realised the denominator $\frac{3 + 8 i \sin θ - 4 \sin^{2} θ}{1 + 4 \sin^{2} θ}$ but don't know how to utilise the knowledge that the expression is purely imaginary.

tambustqaze 2022-04-01

$i \sin (x)$ phase shift
By Euler's formula, I can express i in the following way:
$i = \cos (\frac{π}{2}) + i \sin (\frac{π}{2}) = \exp (i \frac{π}{2})$
I wonder if it is legitimate to write
$i \sin x = \exp (i \frac{π}{2}) \cdot \frac{\exp (i x) - \exp (- i x)}{2 i}$
$= \frac{\exp (i x) \exp (i \frac{π}{2}) - \exp (- i x) \exp (i \frac{π}{2})}{2 i}$
$= \frac{\exp (i (x + \frac{π}{2})) - \exp (- i (x + \frac{π}{2}))}{2 i}$
$= \sin (x + \frac{π}{2})$
I don't feel like this is right, because it would imply a lot of weird things. So where is my mistake?

Sanai Huerta 2022-04-01

Prove that $\frac{\sec 8 A - 1}{\sec 4 A - 1} = \frac{\tan 8 A}{\tan 2 A}$
I tried converting $\sec 4 A$ into $\frac{1}{\cos 4 A}$ and $\sec 8 A$ into $\frac{1}{\cos 8 A}$ but couldn't get the answer. Any help would be appreciated.

markush35q 2022-04-01

Prove that $\frac{\cos 3 A + \cos 3 B}{2 \cos (A - B) - 1} = (\cos A + \cos B) \cos (A + B) - (\sin A + \sin B) \sin (A + B)$
I used $\cos 3 A = 4 \cos^{3} A - 3 \cos A$ , but it is getting more and more complicated.

Alexis Alexander 2022-04-01

Prove that $(1 + 2 \cos \frac{2 x}{3}) \sin \frac{x}{3} = \sin x$ for $x \in R$

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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