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

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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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