If a^2=b^2+c^2-2bcCOSA (the cosine rule) what does COSA equal?

Question

I'm a GCSE Mathematics student and would greatly appreciate any help with this. Thank you.

By 'what does COSA equal' I am asking you to please rearrange the formula so that COSA is the subject. Sorry for any confusion.

Answer 1

a^2=b^2+c^2-2bcCOSA
well,
now taking 2bcCOSA otherside,
b^2+c^2-a^2=2bcCOSA
so,
COSA=b^2+c^2-a^2/2bc
COSB=c^2+a^2-b^2/2ac
COSC=a^2+b^2-c^2/2ab

hope this helps

Answer 2

If a^2=b^2+c^2-2bcCOSA (the cosine rule) what does COSA equal?

A is the angle opposite the side a of the triangle.CosA is the cosine of angle A. The cosine of an angle varies from +1 to 0 as the angle increases from zero degrees to 90 degrees. Then the cosine changes from 0 to -1 as as the angle increases from 90 degrees to 180 degrees. Then as the angle increases from 180 degrees to 270 degrees, the cosine changes from - 1 to 0, and then increses to +1 as the angle increases from 270 degrees to 360 degrees. 360 degrees is the same as 0 degrees and so the process repeats as the angle increases from 360 degrees to 720 degrees etc.

You can get the cosine of any angle by using your calculator, by using a table containing these values, or by going to google search and typing in cos 30 degrees (or whatever angle you want).

Answer 3

The cosine rule is used if you are given 3 sides of the triangle and the angle is unknown OR if you need to find the side opposite a given angle and the other 2 sides. So cos A is the cosine function of angle A between sides b and c and is opposite side a.

Answer 4

Hey Jesse, simply add 2bc.cos A to both sides, thereby keeping the equation in effect unaltered.
then, a^2 + 2bc.cos A = b^2 + c^2
substract a^2 from both sides, then,
2bc.cos A = b^2 + c^2 - a^2
Divide both sides by 2bc, then,
cos A = [b^2 + c^2 - a^2] / 2bc

Note how we operate on the equation such that equity holds AND the required term (in this case cos A) is isolated.

Answer 5

cosA is the ratio of the side adjacent to angle A to the hypotenuse
cosA=[b^2+c^2-a^2]/2bc

Answer 6

a^2=b^2+c^2-2bcCOSA
a^2 -b^2 -c^2 = -2bcCOSA
(a^2 -b^2 -c^2)/-2bc = COSA or
(-a^2 -b^2 +c^2)/2bc = COSA

Answer 7

A is the angle opposite side a
a^2=b^2+c^2-2bcCOS(A)

Answer 8

cos A is THE COSINE OF THE ANGLE OPPOSITE TO SIDE a

& CONTAINED BY SIDES b and c.

Some answers are quite misguiding.
Triangle is not necessarilright angled and so mention of hypotunuse in general is very wrong.

Answer 9

a^2=b^2+c^2-2bcCOSA

a^2 - b^2=c^2-2bcCOSA
a^2 - b^2-c^2=-2bcCOSA
a^2 - b^2-c^2/-2ab=cosA

Answer 10

a^2 = b^2 + c^2 - 2bc(cosA)
cos(A) = (a^2 - b^2 - c^2)/(-2bc)