Precalculus Solutions | Expert Assistance for Problems & Examples

Finding maximum and minimum values of $\sin (2 x) - x for x \in [- \frac{π}{2}, \frac{π}{2}]$

Zugdichte2r 2022-01-27

What is the technique that should be used to evaluate $\int_{0}^{2 π} {(\sin (k \sin θ))}^{2} d θ$ ?

I searched for it and found out that it does

Adrian Cervantes 2022-01-27

Given that
$5 \cos (x) - 12 \sin (x) = 13$
Im

Gabriela Duarte 2022-01-27

Solving a differential equation with trigonometric functions
How could I approach
$y - A \cdot \sin (\frac{d^{2} y}{{d x}^{2}}) = 0$

Wendy Gutierrez 2022-01-27

Solving $\sin x = \sin y$ by using the prosthaphaeresis formulas
$\sin (x) - \sin (y) = 0$
$2 \cos (\frac{x + y}{2}), \sin (\frac{x - y}{2}) = 0$
There are two possibilities $\cos (\frac{x + y}{2}) = 0 or \sin (\frac{x - y}{2}) = 0$
In the first case:
$\frac{x + y}{2} = \frac{π}{2} + k π$
In the second case:
$\frac{x - y}{2} = k π$
The above two equations give the result:
$x = \frac{π}{2} + 2 k π$
$y = \frac{π}{2}$

jelentetvq 2022-01-27

How can I convert the complex number $i^{π}$ to trigonometric form?
I usually do these steps:
1. take Z=a+bi form,
2. find $r = \sqrt{a^{2} + b^{2}}$
3. $\cos (ϕ) = \frac{a}{r}, \sin (ϕ) = \frac{b}{r}$
4. find $ϕ$ from the above 2 equations.

Addison Gross 2022-01-27

Area bounded by $y = \sqrt{\frac{1 + \sin {x}}{\cos {x}}}$ and $y = \sqrt{\frac{1 - \sin {x}}{\cos {x}}}$

Miguel Davenport 2022-01-27

Let $x_{n} = 2^{n} a_{n}$ , and $a_{n + 1} = \sqrt{\frac{1 - \sqrt{1 - a_{n}^{2}}}{2}}, a_{0} = 1$ , how to prove $x_{n}$ converges?

Lainey Goodwin 2022-01-27

Easy way of tackling $\sqrt{x^{2}} + x = \sqrt{5}$
Solve for x

mairie0708zl 2022-01-27

If $\sin x + \sin^{2} x + \sin^{3} x = 1$ , then find $\cos^{6} x - 4 \cos^{4} x + 8 \cos^{2} x$

Gavin Frye 2022-01-27

Two sides of a triangle are $\sqrt{3} + 1 and \sqrt{3} - 1$ and the included angle is $60^{\circ}$ . Find other angles My Attempt Let $a = \sqrt{3} + 1, b = \sqrt{3} - 1$ and $C = 60$ $c^{2} = a^{2} + b^{2} - 2. a . b \cos C$ $= (\sqrt{3} + 1)^{2} + (\sqrt{3} - 1)^{2} - 2 (\sqrt{3} + 1) (\sqrt{3} - 1) . \frac{1}{2} = 8 - 2 = 6$ $⟹ c = \sqrt{6} = \sqrt{2} \sqrt{3}$ $\frac{a}{\sin A} = \frac{c}{\sin C} ⟹ \sin A = \frac{\sqrt{3} + 1}{\sqrt{2} \sqrt{3}} \frac{\sqrt{3}}{2} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ $A = 75^{\circ} & B = 45^{\circ}$ But the solution given in my reference is $105^{\circ}$ and $15^{\circ}$ , what is going wrong with my attempt ?

Kaydence Huff 2022-01-27

Approximating $\cos (47^{\circ})$
Given that $\cos (45^{\circ}) = \frac{\sqrt{2}}{2}$ what would $\cos (47^{\circ})$ be.
Using differential approximation, I get $\cos (47^{\circ})$ is about $\cos (\frac{45 π}{180}) - 2 \sin (\frac{47 π}{180}) = - 0.755600622$ which is of course not right as $\cos (47^{\circ}) = 0.68199836$

m4tx45w 2022-01-27

show that if $β$ is an acute angle and that $\tan β = 2 \sqrt{2}$ then $\cos β = \frac{1}{3}$
This question question has stumped me as I see no obvious way to go with it. This is all Ive

treslagosnv 2022-01-27

Interval in which $(\cos p - 1) x^{2} + \cos p . x + \sin p = 0$ has real roots
The solution given in my reference is the interval $(0, π)$
My Attempt
$Δ = \cos^{2} p - 4 (\cos p - 1) \sin p \geq 0$
$\cos^{2} p - 4 \sin p \cos p + 4 \sin p \geq 0$
$Δ^{'} = 16 \sin^{2} p - 16 \sin p \leq 0 \Rightarrow \sin^{2} p \leq \sin p$

m4tx45w 2022-01-27

Why the periodicity of solution for $θ + γ θ = 0$ implies $\sqrt{γ} = n \in N$
One solution for $θ + γ θ = 0$
is, for $γ > 0$
$Θ (θ) = A \cos \sqrt{γ} θ + B \sin \sqrt{γ} θ$

ardeinduie 2022-01-27

where does the $\cos (θ) = 1 - 2 \sin^{2} (\frac{θ}{2})$ come from?

Adrian Cervantes 2022-01-27

Why $\int_{0}^{2 π} \sin^{2} x d x \neq \int_{0}^{2 π} \sin x \sin n x d x \to n = 1$
By orthogonality, we know that
$\int_{0}^{2 π} \sin m x \sin n x d x = π$ if $m = n$ and 0 otherwise. Nevertheless, when I am calculating it as follows, I get 0.
$\int_{0}^{2 π} \sin x \sin n x d x = \frac{1}{2} {[\frac{\sin [(1 - n) x]}{1 - n} - \frac{\sin [(1 + n) x]}{1 + n}]}_{0}^{2 π}$
But the above quantity is 0 even if n=1. Shouldn't it be $π$ ?

Mlejd5 2022-01-27

How can I prove that $x_{n + 1} = x_{n} \sin (x_{n})$ converges for any $x_{0}$ ?

Madilyn Fitzgerald 2022-01-27

How do I solve this inequality? $3 \sin (2 x) > \sin (x) + \cos (x) + 1$

ndimiimpercea2 2022-01-27

How to prove $\frac{\tan (A)}{\tan (A)} + \frac{\cot (A)}{\cot (A)} = \frac{1}{1 - 2 {\cos (A)}^{2}}$

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