Precalculus Solutions | Expert Assistance for Problems & Examples

Is $\sin (ω t + π) = - \sin ω t$ always true no matter what $ω$ is?
For example, it's true that $\sin (t + π) = - \sin (t)$ . You flip one over the x-axis, and you get the other. But $\sin (2 t + π) = \sin (2 t)$ . Because $\sin (2 t)$ has a period of $π$ , so if you translate it by π, you are still gonna get $\sin (2 t)$

Mina Whitehead 2022-04-16

What is $\arctan (- \tan (θ))$ equal to?

Papierskiix5n 2022-04-16

What is a bound of $\frac{1}{\sin x} - \frac{1}{x}$ on $(0, a]$ ?
Is $\frac{1}{\sin x} - \frac{1}{x}$ bounded in $(0, a]$ , $a < \frac{π}{2}$ ?

delitzo1d4 2022-04-16

How do you factor $x^{3} - 3 x^{2} + 3 x - 1$

Aiyana Ayers 2022-04-16

How do I solve this equation $R$ :
$3 \sin^{3} x + 2 \cos^{3} x = 2 \sin x + \cos x$

Aliyah Mendez 2022-04-16

How do I rewrite $({(\cos t)}^{3}) - 2 ((\cos t) \cdot ({(\sin t)}^{2}))$ to $3 {(\cos t)}^{3} - 2 \cos t$ ?

Leia Sullivan 2022-04-15

Is there a way to find the exact value of the product
$P = \prod_{n = 1}^{1007} \sin (\frac{n π}{2015})$

Angelina Proctor 2022-04-15

Is $x^{4} + 4$ an irreducible polynomial?

Boston Fitzgerald 2022-04-15

Is $\cot^{- 1} (- \cot x)$ equal to -x?

Dakota Livingston 2022-04-15

Is $\cos^{2} θ$ the same as ${(\cos θ)}^{2}$
I am trying to find $lim_{x \to 0} \sin \frac{1}{x}$
I'm assuming it's possible with trigonometric identities. Doing some research, I found that $\sin θ = \pm \sqrt{1 - \cos^{2} θ}$ . However I'm a bit confused on what is $\cos^{2}$ .
Is $\cos^{2} θ$ the same as ${(\cos θ)}^{2}$ ?

Joaquin Salas 2022-04-15

How do I prove that $\frac{\sin (α - β)}{\sin α - \sin β} = \frac{\sin α + \sin β}{\sin (α + β)}$
Using double angle and addition formulas, I simplified the LHS to $\frac{\cos \frac{α - β}{2}}{\cos \frac{α + β}{2}}$

Saul Cochran 2022-04-15

For $x \in (0, \frac{π}{2})$ find a minimal value, which the expression
$\sec x + \csc x + \sec^{2} x + \csc^{2} x$
can take.

Markelovnsl 2022-04-15

Find the maximum value of f(x) where
$f (x) = 2 \cos 2 x + 4 \sin x$ for $0 < x < π$

ds522stlk 2022-04-15

Find the maximum value of
$4 \sin^{2} x + 3 \cos^{2} x + \sin (\frac{x}{2}) + \cos (\frac{x}{2})$

Jazmin Strong 2022-04-15

Find the limit
$lim_{x \to 2} \frac{\sin^{2} (x^{2} - 4) \sec^{2} (3 x - 6)}{(x^{3} - 8) \tan (2 x - 4)}$

Markelovnsl 2022-04-15

Find ${\sin 81}^{\circ}$ given ${\sin 18}^{\circ} = \frac{\sqrt{5} - 1}{4}$
a) $\frac{\sqrt{5} + 1}{4}$
b) $\frac{\sqrt{3 + \sqrt{5}} + \sqrt{5 - \sqrt{5}}}{4}$
c) $\frac{\sqrt{10 + 2 \sqrt{5}}}{4}$
${\cos 18}^{\circ} = \sqrt{1 - \frac{6 - 2 \sqrt{5}}{16}} = \frac{\sqrt{10 + 2 \sqrt{5}}}{4}$
${\sin 81}^{\circ} = {\cos 9}^{\circ} = \sqrt{\frac{1 + {\cos 18}^{\circ}}{2}} = \sqrt{\frac{4 + \sqrt{10 + 2 \sqrt{5}}}{8}} = \frac{\sqrt{8 + 2 \sqrt{10 + 2 \sqrt{5}}}}{4}$

Tyson Mcneil 2022-04-15

Find explicit form of y
I was solving a differential equation and I get this as a result:
$\frac{4}{3} \ln x + c = \sin (\frac{y^{2}}{x^{2}} - 1)$
Is this enough as solution? Or how can show the solution in the form of $y = f (x)$

Bryanna Leon 2022-04-15

How do I show that $\frac{1}{{(1 - \cos {θ})}^{2}} = {\frac{14}{\csc}}^{4} {\frac{1}{2}} θ$
I've tried fiddling around with half angle formulae but can't get the required result.

Breanna Fisher 2022-04-15

How do I simplify
$\sqrt{3} ({\cot 70}^{\circ} + 4 {\cos 70}^{\circ})$

Ean Hughes 2022-04-14

Minimum value of $h (θ) = 3 \sin θ - 4 \cos θ + \sqrt{2}$
Find the minimum value of $h (θ)$
$h (θ) = 3 \sin θ - 4 \cos θ + \sqrt{2} = 5 \sin (θ + 53.13) + \sqrt{2}$
Minimum value - $5 \sin (θ + 53.13) + \sqrt{2} = - 5$
Therefore min value is = $- \frac{5}{5} - \sqrt{2}$
Why am I wrong ?

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