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Nutka1998 [239]

3 years ago

14

Simplify 1-5/4(6t-3/4)+3(17-5/17)

1 answer:

Firlakuza [10]3 years ago

8 0

-15t/2 + 14159/272

I'm not exactly sure what you are looking for, but this is what I got.

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Find sin θ if cos θ = 4/7 and θ in quadrant IV. Give an exact answer.

11111nata11111 [884]

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\
-------------------------------\\\\
cos(\theta)=\cfrac{4}{7}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}
\\\\\\
\textit{using the pythagorean theorem to get the opposite side or "b"}
\\\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{7^2-4^2}=b
\\\\\\
\pm \sqrt{33}$

now, the square root gives us both +/- versions, which is it? well, we know the angle θ is in the IV quadrant, well, the sine is "b" is negative there, thus is the negative version then

thus $\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(\theta)=\cfrac{-\sqrt{33}}{7}$

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4 years ago