Precalculus Solutions | Expert Assistance for Problems & Examples

Prove that $\sum_{n = 1}^{\infty} \log \cos (\frac{1}{n})$ converges absolutely.

Clarence Hines 2022-01-25

Simplifying $\frac{\sum_{i = 1}^{i = n} 1 + \tan^{2} θ_{i}}{\sum_{i = 1}^{i = n} 1 + \cot^{2} θ_{i}}$ , where $θ_{i} = \frac{2^{i - 1} π}{2^{n} + 1}$

Courtney Griffin 2022-01-25

In any triangle is $\sin A + \sin B + \sin C = \frac{3 \sqrt{3}}{2}$ always Well, I came with an interesting proof. But I just want to verify it Applied at function $y = \sin x$ We have, $\sin (\frac{A + B + C}{2}) \geq \frac{\sin A + \sin B + \sin C}{3}$ From here we will get $\sin A + \sin B + \sin C \leq \frac{3 \sqrt{3}}{2}$ Also by A.M. $\geq$ G.M. in an acute angled triangle $\frac{\sin A + \sin B + \sin C}{3} \geq \sqrt[3]{\sin A \sin B \sin C}$ $\Rightarrow \sin A + \sin B + \sin C \geq 3 (\sqrt[3]{\sin A \sin B \sin C})$ $\Rightarrow \sin A + \sin B + \sin C \geq 3 (\frac{\sqrt{3}}{2}) = \frac{3 \sqrt{3}}{2} > 2$ and from this I get $\sin A + \sin B + \sin C \geq \frac{3 \sqrt{3}}{2}$

Laney Spears 2022-01-25

Adding two cosine waves, result in the standard $A \cdot \cos (ω t + B)$ form
$y (t) = \cos (40 t) - 0.3 \cos (40 t - 16)$
This combines two waves of the same frequency but different phases, and the objective here is to add them and present the result in the simplified form, as a single real amplitude multiplied by a single cosine. I have tried complex analysis, via $R e [e^{i 40 t} (1 - 0.3 e^{- i 16})]$ , but I still can't get a result out of it.

logosomatw 2022-01-25

Find the least value of $\sec^{6} x + \csc^{6} x + \sec^{6} x \csc^{6} x$

Keaton Good 2022-01-25

Can $\cos (36^{\circ})$ be calculated using known cosines like $\cos (37^{\circ})$ and the derivative formula
$f^{'} (x) \approx \frac{f (x + △ x) - f (x)}{△ x}$

Duncan Reed 2022-01-25

Finding the fundamental period of $- 6 \cos (5 π x)$
I am trying to find the fundamental period of $f (x) = - 6 \cos (5 π x)$ . I know a periodic function satisfies f(x)=f(x+p).
I know that $\cos (x)$ 's periodicity is $2 π$ as $\cos (x + 2 π) = \cos (x)$ so I just assumed that $- 6 \cos (5 π \cdot 1 + 2 π) = - 6 \cos (5 π)$ , which it is but apparently this is not correct for the fundamental period?

Lainey Goodwin 2022-01-25

How do I show ${(\csc θ - \cot θ)}^{2} \equiv \frac{1 - \cos θ}{1 + \cos θ}$ ?

Ahmed Stewart 2022-01-25

Proving $\frac{1 + \cos x}{2 + \sin x} < \frac{4}{3}$

maliaseth0 2022-01-25

Is the phase shift of $- 3 \sin (2 x + \frac{π}{2}) + 1$ equal to $- \frac{π}{4}$ or just $- \frac{π}{2}$ ?

William Montgomery 2022-01-25

Find $\cot (\sum_{n = 1}^{23} \cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$
I tried to simplify it but it became messy. How can I find $\sum_{n = 1}^{23} \cot^{- 1} (1 + n + n^{2}) ?$

Marquis Neal 2022-01-25

Can this equation be solved? $x + \sin (x) = \frac{11 π}{48}$

Kayleigh Dixon 2022-01-25

Graph of $7 \cos x + 5 \sin x = 2 k + 1$
The question is to find the number of integral values of k for which the equation
$7 \cos x + 5 \sin x = 2 k + 1$ has a solution.
I have solved it by converting the LHS into $\sqrt{74} \sin (x + α)$ , where $α = \arctan (\frac{7}{5})$ . And then making an inequality with RHS.

Zugdichte2r 2022-01-25

If $\tan x = 3$ , then what is the value of $\frac{3 \cos 2 x - 2 \sin 2 x}{4 \sin 2 x + 5 \cos 2 x}$ ?

licencegpopc 2022-01-25

Find the value of the function $\frac{\cos (α - β)}{2}$
I solved it by squaring the two equations such that I get $\sin^{2} α + \sin^{2} β + 2 \sin α \sin β = \frac{441}{4225}$ And $\cos^{2} α + \cos^{β} + 2 \cos α \cos β = \frac{729}{4225}$
Adding them we get $2 + 2 (\sin α \sin β + \cos α \cos β) = \frac{1170}{4225}$
Then, $1 + \cos (α - β) = \frac{585}{4225}$
Therefore $\cos (α - β) = - \frac{3640}{4225}$
So now $\frac{\cos (α - β)}{2} = + or - \sqrt{\frac{585}{8450}}$

Write the given expression without the absolute value symbol. |x − y| − |y − x|

Jamya Elliott 2022-01-24

How do you write $y = \frac{1}{x^{2} + 3}$ as a composition of two simpler functions?

estadsocm3 2022-01-24

If $f (x) = 2 x - 9 and g (x) = {(x + 1)}^{2},$ what is the composite function $f (g (x))$

Isis Solis 2022-01-24

Suppose that $f (x) = - 4 - 3 x$ and $g (x) = \sqrt{2} + x$ find the rule of the composite function $f \circ g$ ?

Emmy Combs 2022-01-24

How do you write $k (x) = e^{\sin x}$ as a composition of two or more functions?

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