Precalculus Solutions | Expert Assistance for Problems & Examples

Given $3 \cos x - 4 \sin x = 2$ find $3 \sin x + 4 \cos x$ without first solving for x

encaderpwp 2022-03-25

Given an angle $θ$ , the formulas for $\sin (\frac{θ}{2})$ and $\cos (\frac{θ}{2})$ are either positive or negative, which is why $\pm$ is used in their formulas. So, if $\tan (\frac{θ}{2}) = \frac{\sin (\frac{θ}{2})}{\cos (\frac{θ}{2})}$ , and both the numerator and denominator are either positive or negative (and unless $θ$ is defined, we must assume they can be both), shouldn't the formula for $\tan (\frac{θ}{2})$ also be $\pm$ ?
Below are the equations I am referring to.
$\sin (\frac{u}{2}) = \pm \sqrt{\frac{1 - \cos (u)}{2}}$
$\cos (\frac{u}{2}) = \pm \sqrt{\frac{1 + \cos (u)}{2}}$
$\tan (\frac{u}{2}) = \frac{1 - \cos (u)}{\sin (u)} = \frac{\sin (u)}{1 + \cos (u)}$

Lesnaoq73 2022-03-25

General solution of $(\sqrt{3} - 1) \sin θ + (\sqrt{3} + 1) \cos θ = 2$

tambustqaze 2022-03-25

Given
$\sin (10^{100}) + \sin (n) = 0$
find n.

kembdumatxf 2022-03-25

Further simplify $\tan (α + β) - \tan (β)$
but I keep wondering, whether it's possible to further simplify this, into for example only using the $\tan$ once. I tried using the addition theorems for trigonometry, but these just seem to complicate them further.
I already tried something along this:
$r = \tan (α + β) - \tan (β)$
$= \frac{\tan α + \tan β}{1 - \tan α \tan β} - \tan β$
$= \frac{\tan α + \tan β}{1 - \tan α \tan β} - \frac{(1 - \tan α \tan β) (\tan β)}{1 - \tan α \tan β}$
$= \frac{(\tan α + \tan β) - (\tan β - \tan α \tan^{2} β)}{1 - \tan α \tan β}$
$= \frac{\tan α + \tan α \tan^{2} β}{1 - \tan α \tan β}$

Find a polynomial f(x) of degree 5 that has the following zeros 9, -2 , 8, 6, -5 Leave answer in factored form

Jasmine Todd 2022-03-24

How do I find out the value of p for $\sin p + \cos p = 0$ ?

markush35q 2022-03-24

How can we prove this identity:
$\sum_{n = 1}^{\infty} \arctan \frac{{(- 1)}^{n}}{ϕ^{2 n + 1}} = \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{\sqrt{5}, ϕ^{4 n - 2}, (2 n - 1), F_{2 n - 1}}$
where $F_{n}$ are the Fibonacci numbers, and $ϕ = \frac{1 + \sqrt{5}}{2}$ is the golden ratio?

monkeyman130yb 2022-03-24

How can one tell the period of $\sin (x^{\frac{3}{2}})$ ? Is it ${(2 π)}^{\frac{2}{3}}$ ?

Polchinio3es 2022-03-24

How can I write the
$\cos^{5} (x)$
as a sum of first order terms? I have started noticing that:
$\cos^{5} (x) = \cos^{4} (x) \cos (x)$
and then:
$\cos^{4} (x) = \cos^{2} (x) \cos^{2} (x)$
Finally:
$\cos^{2} (x) = \frac{1}{2} (1 + \cos (2 x))$
But I would like to find an easier formula, like the one for
$\cos^{2} (x)$

ashes86047xhz 2022-03-24

How can I prove $\sqrt{\sin^{2} (x)} \neq \sin (x)$

Beryneingmk39 2022-03-24

How can I find the value of
$\sin^{24} \frac{π}{24} + \cos^{24} \frac{π}{24}$

Tony Mccarthy 2022-03-24

Help with $\int \frac{1 + \sin x}{(1 + 2 \cos x) \sin x} d x$

Oxinailelpels3t14 2022-03-24

Given the following expression
$w = j \cos [\frac{1}{n} \arccos (\frac{j}{e}) + \frac{m π}{n}] = j \cos (z)$

Kiara Haas 2022-03-24

Given that A,B,C be angles in an acute triangle.
If $(5 + 4 \cos A) (5 - 4 \cos B) = 9$ and $(13 - 12 \cos B) (13 - 12 \cos C) = 25$
find $\cos (A + C)$ . I know $A + B + C = 180^{\circ}$ and $\cos B = - \cos (A + C)$ and what next?

Pablo Dennis 2022-03-24

Given that ${\cos 160}^{\circ} = - q$ , express ${\cos 70}^{\circ}$ in terms of q.

nomadzkia0re 2022-03-24

Given $x = \frac{2 π}{1999}$
Find the value of
$\cos x \cos 2 x \cos 3 x \dots \cos 999 x$

Polchinio3es 2022-03-24

Formula for $\sin {\frac{θ}{3}}$
Using $\sin {3 θ} = 3 \sin {θ} - 4 \sin^{3} {θ}$ ,we may calculate $\sin {\frac{θ}{3}}$
But the formula for root of a cubic equation is very complicated can you help me to find a formula for $\sin {\frac{θ}{3}}$ as it will help to compute ${\sin 20}^{\circ}, {\sin 10}^{\circ}$ etc. which will be useful.

Kendall Daniels 2022-03-24

Let x and y be real numbers such that $\frac{\sin x}{\sin y} = 3$ and $\frac{\cos x}{\cos y} = \frac{1}{2}$ . The value of $\frac{\sin 2 x}{\sin 2 y} + \frac{\cos 2 x}{\cos 2 y}$ can be expressed in the form $\frac{p}{q}$ , where p and q are relatively ' positive integers. Find p+q.

siliciooy0j 2022-03-24

Let $A = {(2 \sin \frac{7 π}{18} + 1)}^{2556}$
How can one find the remainder from the division of [A] by 17?

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.

Precalculus

Solve Precalculus Problems | Expert Help Available