Precalculus Solutions | Expert Assistance for Problems & Examples

How to prove the following equation by a quick method?
$\sin^{6} x + \cos^{6} x = \frac{1}{8} (3 \cos 4 x + 5)$

Adison Palmer 2022-04-06

How to prove $\sin 3 θ = 3 \sin θ - 4 \sin^{3} θ$

Kasey Castillo 2022-04-06

How to prove ${\cos 36}^{\circ} = \frac{1 + \sqrt{5}}{4}$

Gustavo Lam 2022-04-06

How to prove $\cos (n!) \neq 1$ without using $π$ is irrational

Julian Peck 2022-04-06

How to proof
$\arcsin (\sqrt{2 \cdot b \cdot (\sqrt{1 + b^{2}} - b)}) = \arccos (\sqrt{1 + b^{2}} - b)$

Jaylen Cantrell 2022-04-06

How to know all the roots for fourth degree equation like this :
$- 8 x^{4} - 18 x^{2} - 11 + \frac{1}{x^{4}} = 0$

Mary Bates 2022-04-06

How to graph $f (x) = \frac{1 - \cos (2 x - 2)}{{(x - 1)}^{2}}$ analytically?
I only have an issue when it comes to determining the hole at $x = 1$ analytically. Graphing the function on a graphing utility reveals a hole at $x = 1$ rather than a vertical asymptote. I know that by simply plugging in the value $1$ for $x$ , one will see that both the numerator and denominator equate to zero. This shows that there is at least one factor of $(x - 1)$ that can be extracted from the numerator.
I would like to know how to simplify this function analytically in such a way that two factors of $(x - 1)$ can be obtained from the numerator. I believe one must make use of an inverse function down the line in order to extract the obvious $(x - 1)$ hiding in the $\cos (2 x - 2) = \cos (2 (x - 1))$ term. That is as far as I got in the problem.

Brielle James 2022-04-06

How to get $\frac{2}{t^{2} + 1}$ as the derivative for $\sin (θ)$ when $\tan (\frac{θ}{2}) = t$

The subset of matrices in the vector space 𝑀𝑛,𝑛 of 𝑛 × 𝑛 matrices whose diagonal elements sum to 0.

Brooks Barker 2022-04-05

For n real numbers $x_{1}, x_{2}, \dots, x_{n}$ , consider
$a = \sin (x_{1}) \cos (x_{2}) + \sin (x_{2}) \cos (x_{3}) + \dots + \sin (x_{n}) \cos (x_{1})$
How do we find maximum value of a?
For what values of $x_{1}, x_{2} \dots ., x_{n}$ is the maximum achieved?
I want to get help from you If that's possible.

Abbey Ellison 2022-04-05

Finding real roots of $P (x) = x^{8} - x^{7} + x^{2} - x + 15$

Hallie Watts 2022-04-05

Finding $\cos (\frac{π}{8})$ with half angle identities.

Yaritza Estrada 2022-04-05

Finding all values of $\sin (x - 50^{\circ}) = - 0.682$ between $0^{\circ}$ and $360^{\circ}$

ds522stlk 2022-04-05

Find value of $\tan 1 \times \tan 2 \times \dots \times \tan 89$ . Please don't answer, but please help me to figure this out this as I am not aware of any method to calculate this. I tried it by finding value of $\tan (90^{\circ})$ , but it didn't work as $\tan (90^{\circ})$ is not-defined.

Malachi Mullins 2022-04-05

Find value of $\tan (\frac{π}{25}) \cdot \tan (\frac{2 π}{25}) \dots \tan (\frac{12 π}{25})$
The solution I tried:
Assume
$P = \tan (\frac{π}{25}) \cdot \tan (\frac{2 π}{25}) \cdot \tan (\frac{3 π}{25}) \dots \dots \tan (\frac{12 π}{25})$ ,
with the help of $\tan (π - θ) = - \tan θ$ , then
$P = \tan (\frac{13 π}{25}) \cdot \tan (\frac{14 π}{25}) \cdot \tan (\frac{15 π}{25}) \dots \dots \tan (\frac{24 π}{25})$
which gives
$P^{2} = \prod_{{r = 1}}^{24} \tan (\frac{r π}{25})$

Ashleigh Mitchell 2022-04-05

Find the value(s) of $θ$ such that: $\sin (θ + 30^{\circ}) = {\cos 50}^{\circ}$

Joaquin Salas 2022-04-05

Find the value of $\sin (\frac{1}{4} \arcsin \frac{\sqrt{63}}{8})$

Haylee Bowen 2022-04-05

Find the value of F
${(\frac{1.5}{F})}^{2} + \cos^{2} (75) + {(\frac{1.25}{F})}^{2} = 1$

Miguel Hanson 2022-04-05

Find the value of
$({\cos 52}^{\circ} + {\cos 68}^{\circ} + {\cos 172}^{\circ})$

Quinn Moses 2022-04-05

Find the solutions of
$\sin z = 3$

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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