Sin30+sin60+sin90 ÷ cos30+cos60+cos90?

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Sin30+sin60+sin90 ÷ cos30+cos60+cos90?

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Answer 1 · 2018-04-11T13:07:05

$\frac{6 + 7 \sqrt{3}}{6}$ $(6+7sqrt3)/6$

(Are you sure you didn't miss out brackets somewhere? Is this what you meant? $\frac{sin 30 + sin 60 + sin 90}{cos 30 + cos 60 + cos 90}$ $(Sin30+sin60+sin90) / (cos30+cos60+cos90)$ . Because the answer to this is $\sqrt{3}$ $sqrt3$ which seems a lot nicer and more likely)

Explanation:

$sin 30 = \frac{1}{2}$ $sin30=1/2$
$sin 60 = \frac{\sqrt{3}}{2}$ $sin60=sqrt(3)/2$
$sin 90 = 1$ $sin90=1$
$cos 30 = \frac{\sqrt{3}}{2}$ $cos30=sqrt3/2$
$cos 60 = \frac{1}{2}$ $cos60=1/2$
$cos 90 = 0$ $cos90=0$

Now, you have to follow the order of operations (BIDMAS):

Brackets
Indices
Division
Multiplication
Addition
Subtraction

As you can see, you do division before addition, so you must do $\frac{sin 90}{cos 30}$ $sin90/cos30$ before anything else.

$\frac{sin 90}{cos 30} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2 \sqrt{3}}{3}$ $sin90/cos30=1/(sqrt3/2)=(2sqrt3)/3$

Now add the other values

$\frac{2 \sqrt{3}}{3} + \frac{1}{2} + \frac{\sqrt{3}}{2} + \frac{1}{2} + 0 = \frac{6 + 7 \sqrt{3}}{6}$ $(2sqrt3)/3+1/2+sqrt3/2+1/2+0=(6+7sqrt3)/6$

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Sin30+sin60+sin90 ÷ cos30+cos60+cos90?

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