Precalculus Solutions | Expert Assistance for Problems & Examples

We all know that $\cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}, \cos (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ and $\cos (\frac{π}{3}) = \frac{1}{2}$ . One can also prove that $\cos (\frac{π}{5}) = \frac{\sqrt{5} + 1}{4}$ . But it seems that $\cos (\frac{π}{7})$ cannot be put in a closed form algebraic expression. Is there a proof of such a claim? I feel like this has to do with the Abel–Ruffini theorem.
The same for $\cos (\frac{π}{8})$ and $\cos (\frac{π}{9})$ . But $\cos (\frac{π}{10}) = \sqrt{\frac{5}{8} + \frac{\sqrt{5}}{8}}$

Dania Robbins 2022-04-21

Verify:
$\sec^{2} x + \tan^{2} x = (1 - \sin^{4} x) \sec^{4} x$

p3sa1bynn 2022-04-21

Value of ${\cos 20}^{\circ} + 2 \sin^{2} 55^{\circ} - \sqrt{2} {\sin 65}^{\circ}$

Davian Lawson 2022-04-21

Value of ${\cos 52}^{\circ} + {\cos 68}^{\circ} + {\cos 172}^{\circ}$ ?

vacinammo288 2022-04-21

Using implicit differentiation, find y' if $\sin (x + y) = y^{2} \cos (x)$

zamenjenot7k 2022-04-21

Using the formula for $\sin (A + B)$ and $\cos (A + B)$ show that:
$\frac{\cos (A - B) - \cos (A + B)}{\sin (A - B) - \sin (A + B)} = \tan (A)$
anybody knows how to get the answer? I keep getting stuck at $\frac{2 \sin (A) \sin (B)}{2 \cos (A) \cos (B)}$

Michael Rivers 2022-04-21

Solve $lim_{x \to \infty} \frac{x + \sin (x)}{2 x + \cos (x)}$

Wissety52 2022-04-21

Solve:
$2 + \cos \frac{3 x}{2} + \sqrt{3} \sin \frac{3 x}{2} = 4 \sin^{2} \frac{x}{4}$

ulcerat9jr 2022-04-21

Solve $\frac{d y}{d x} = \cos (x + y) + \sin (x + y)$
My Attempt
$\frac{d y}{d x} = \sqrt{2} \cos (x + y - \frac{π}{4})$
Set $t = x + y - \frac{π}{4} \Rightarrow y = t - x + \frac{π}{4}$
$\frac{d y}{d x} = \frac{d t}{d x} - 1 = \sqrt{2} \cos t$
$\frac{d t}{d x} = \sqrt{2} \cos (t) + 1$
$\int \frac{d t}{\sqrt{2} \cos (t) + 1} = \int d x$
How do I proceed further to find the general solution ?

Kymani Shepherd 2022-04-21

Solve for x where $0 \leq x \leq 360$
$2 \sin x = \tan x$
I tried this and I ended up with
$\cos x = 2$
Steps: $\sin x = \frac{\tan x}{2}$
$\sin x = \frac{\frac{\sin x}{\cos x}}{2}$
$\sin x = \frac{\cos x}{2} \sin x$
$2 = \cos x$
to find x I did $\cos^{- 1}$ , but $\cos^{- 1} 2$ is a math error

abiejose55d 2022-04-21

Solve for x: $1 + \tan^{2} (x) = 8 \sin^{2} (x), x \in [\frac{π}{6}, \frac{π}{2}]$

kulisamilhh 2022-04-21

Solve
$\sin x + \cos x + \tan x + \csc x + \sec x + \cot x = - 2$
from $0 < x < 2 π$

vacinammo288 2022-04-20

If $0 \leq θ \leq 360$ , and:
$\cos (θ - 35.54) = \frac{8}{\sqrt{74}}$

tobeint39r 2022-04-20

If $\cos^{6} (x) + \sin^{6} (x) = a + b \cos (4 x)$ . Find ab?
As after solving above equation, I get $1 - 3 \sin^{2} (x) \cos^{2} (x) = a + b \cos (4 x)$ . Please help me to solve this problem.

Kason Chang 2022-04-20

If $α, β, γ$ are the zeros of $x^{3} + 4 x + 1$ , then calcu;ate the value of:
$(α + β) - 1 + (β + γ) - 1 + (γ + α) - 1$

kadetskihykw 2022-04-20

If $\cos (θ) = - \frac{2}{3}$ and $450^{\circ} < θ < 540^{\circ}$ , find
1. The exact value of $\cos (\frac{1}{2} θ)$
2.The exact value of $\tan (2 θ)$

Jazmine Sweeney 2022-04-20

How to find value of this sum?
$\sum_{m = 1}^{\infty} \tan^{- 1} (\frac{2 m}{m^{4} + m^{2} + 2})$

spetterde52g 2022-04-20

If a,b,c are in an Arithmetic Progression (AP), prove that
$\frac{\sin {c} - \sin {a}}{\cos {a} - \cos {c}} = \cot {b}$

Caitlyn Cole 2022-04-20

How to find the integral
$\int_{0}^{70 π} | \cos^{2} x \sin x | d x$

Gage Potter 2022-04-20

How to find : $lim_{x \to \frac{1}{4}} \frac{1 - \tan (π x)}{2 x - \sqrt{x}}$

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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