$\bf cos^{-1}\left( \cfrac{1}{8} \right)=\theta \qquad \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{8}}\impliedby \textit{let's find the \underline{opposite}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{8^2-1^1}=b\implies \pm\sqrt{63}=b ~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{\pm\sqrt{63}}}{\stackrel{adjacent}{1}} \\\\\\ ~\hspace{34em}$

$\bf \stackrel{\textit{keeping in mind that}}{tan\left(cos^{-1}\left( \frac{1}{8} \right) \right)}\implies tan(\theta )$

5 0

3 years ago

Find the radius of a circle whose circumference is 31.4 centimeters. Approximate Π as 3.14.

sladkih [1.3K]

The circumference of every circle is (pi) times (diameter).

The diameter is (2 x radius), so we can write

Circumference = (pi) x (2 x radius) .

The question gives us the circumference, and the number to use for (pi).
I shall now pluggum in:

(31.4 cm) = (3.14) x (2 x radius)

Divide each side by 3.14: (31.4 cm)/(3.14) = 2 x radius

Divide each side by 2 : (31.4 cm) / (2 x 3.14) = radius

5 cm = radius

8 0

3 years ago

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