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

1 Answer
BB
Apr 11, 2018

(6+7sqrt3)/6

(Are you sure you didn't miss out brackets somewhere? Is this what you meant? (Sin30+sin60+sin90) / (cos30+cos60+cos90). Because the answer to this is sqrt3 which seems a lot nicer and more likely)

Explanation:

sin30=1/2
sin60=sqrt(3)/2
sin90=1
cos30=sqrt3/2
cos60=1/2
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 sin90/cos30 before anything else.

sin90/cos30=1/(sqrt3/2)=(2sqrt3)/3

Now add the other values

(2sqrt3)/3+1/2+sqrt3/2+1/2+0=(6+7sqrt3)/6

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