Precalculus Solutions | Expert Assistance for Problems & Examples

Solving $2 \cos 2 x - 4 \sin x \cos x = \sqrt{6}$

ideklaraz7xz 2022-04-02

Solving $2 \sin^{2} x + 6 \sin^{2} \frac{12}{x} = 3$
Find the angles between $0^{\circ} and 360^{\circ}$ which satisfy the equation above.
So, I found the answers by inputting all the possible special angles; $60^{\circ} and 120^{\circ}$ worked.
Are there any other ways to find the answers, and are there more than the two answers that I found?

justbethlflql 2022-04-02

Solving $\sin (3 x + 28^{\circ}) = \cos (2 x - 13^{\circ})$
Solution:
3x+28+2x-13=90
x=15
3x+28-2x+13=90
x=49
But the value
x=87
also satisfies the equation. I do not know how it comes.

Rex Maxwell 2022-04-02

Solving $\cos x + \cos 2 x - \cos 3 x = 1$ with the substitution $z = \cos x + i \sin x$

Aryan Salinas 2022-04-02

Solving for k in $\cos \frac{π}{k} - \cos \frac{2 π}{k} = P$

annlanw09y 2022-04-02

Prove that $\frac{1 + \sin θ + i \cos θ}{1 + \sin θ - i \cos θ} = \sin θ + i \cos θ$

diartrosiwk8o 2022-04-02

Prove that if x,y are rational numbers and
$x^{5} + y^{5} = 2 x^{2} y^{2}$

ropowiec2gkc 2022-04-02

Prove that
$1 + m \cos 2 θ + (\begin{matrix} m \\ 2 \end{matrix}) \cos 4 θ + \dots + (\begin{matrix} m \\ r \end{matrix}) \cos 2 r θ + \dots + \cos 2 m θ = 2^{n} \cos^{m} θ \cos m θ$

Dominique Pace 2022-04-02

Prove that
$x^{8} - x^{7} + 2 x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{2} - 4 x + \frac{5}{2} \geq 0$ for all real x

Reuben Brennan 2022-04-02

Prove that
$3 {(\sin θ - \cos θ)}^{4} + 6 {(\sin θ + \cos θ)}^{2} + 4 (\sin^{6} θ + \cos^{6} θ) - 13 = 0$

Lorelei Stanton 2022-04-02

Prove that
$\sin^{2} α + 4 \sin^{4} \frac{α}{2} = 4 \sin^{2} \frac{α}{2}$

jermandcryspza3 2022-04-02

Prove that
$\frac{1}{\sin^{2} \frac{π}{4 k + 2}} + \frac{1}{\sin^{2} \frac{3 π}{4 k + 1}} + \frac{1}{\sin^{2} \frac{5 π}{4 k + 2}} + \dots + \frac{1}{\sin^{2} \frac{(2 k - 1) π}{4 k + 2}} = 2 k (k + 1)$

A polynomial f(x) with real coefficients and leading coefficient 1 has the given zero and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
7 + 8i; degree 2

Isaac Hampton 2022-04-01

I need help proving the following identity.
$\tan^{2} 10^{\circ} + \tan^{2} 50^{\circ} + \tan^{2} 70^{\circ} = 9$

London Douglas 2022-04-01

I have this equation
$\frac{1 - e^{2}}{1 + e \cos (θ - θ_{0})} = 1 - e \cos η$
and using the identity
$\cos θ = \frac{1 - \tan^{2} \frac{θ}{2}}{1 + \tan^{2} \frac{θ}{2}}$
this becomes
$\sqrt{1 - e} \tan (\frac{θ - θ_{0}}{2}) = \sqrt{1 + e} \tan \frac{η}{2}$
However, I'm unsure about the steps in between.

ikramkeyslo4s 2022-04-01

I have the following function:
$f (x) = \sqrt{3} \cos (x) + \sin (x)$
I am trying to find what the amplitude of this function is without graphing it. I understand the formula for a cosine equation is:
$y = A \cos (B x - C)$

Ashleigh Shaffer 2022-04-01

I have the following equation:
$\frac{138000}{{(1 + x)}^{5}} + \frac{71000}{{(1 + x)}^{4}} + \frac{54000}{{(1 + x)}^{3}} + \frac{37000}{{(1 + x)}^{2}} + \frac{20000}{1 + x} - 20000 = 0$

acidizihvzs 2022-04-01

I have
$\frac{\tan 15 °}{1 - \tan {15^{\circ}}^{2}}$

Samara Richard 2022-04-01

Someone can explain me why
$\tan (- \frac{π}{4} + \arctan x) = \frac{x - 1}{x + 1}$

Rex Maxwell 2022-04-01

I am trying to find absolute maximum and absolute minimum values for $f (x) = \cos (x) + \sin (2 x)$ on the interval $[0, \frac{π}{2}]$
I started off by finding the derivative:
$f^{'} (x) = - \sin x + 2 \cos (2 x)$
Then I tried to find the critical numbers. But that's where I ran amuck. I came up with:
$\sin x = 2 \cos (2 x)$
How do I go about solving for 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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