The word you're looking for is "differentiate", not "derive".

$\dfrac{\mathrm d}{\mathrm dw}\ln(\cos(w-1))=\dfrac{\frac{\mathrm d}{\mathrm dw}\cos(w-1)}{\cos(w-1)}=\dfrac{-\sin(w-1)\frac{\mathrm d}{\mathrm dw}(w-1)}{\cos(w-1)}=-\dfrac{\sin(w-1)}{\cos(w-1)}=-\tan(w-1)$

3 0

4 years ago

The angle θ lies in Quadrant II .

Andreyy89

let's keep in mind that, in the II Quadrant, cosine is negative and sine, is positive.

cosine is adjacent/hypotenuse, however the hypotenuse is simply a radius unit, and thus is never negative, so in the -(2/3) the negative must be the numerator, -2.

$\bf cos(\theta )=\cfrac{\stackrel{adjacent}{-2}}{\stackrel{hypotenuse}{3}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{3^2-(-2)^2}=b\implies \pm\sqrt{5}=b\implies \stackrel{\textit{II Quadrant}}{+\sqrt{5}=b}~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{5}}}{\stackrel{adjacent}{-2}} \\\\\\ ~\hspace{34em}$

6 0

4 years ago

Using synthetic division, what is the factored form of this polynomial x^3+3x^2-13x-15

kotegsom [21]

Answer:

Step-by-step explanation:

(x-3)(x+1)(x+5)

3 0

3 years ago

Seventeen consecutive positive integers have a sum of 306. What is the sum of the seventeen consecutive integers that immediatel

Stels [109]

Answer:

595

Step-by-step explanation:

Each of the following 17 is 17 more than its corresponding integer in the 1st 17.

---> 306 + 289 = 595

8 0

3 years ago