A few days ago

vaiogirl

What is the exact value of cos 105 degrees?

exact value in radian?

Top 5 Answers

A few days ago

bozmajjeh

Favorite Answer

The correct way to this problem is to somehow change 105º to some degree that we know the exact values of and take it from there. We know the exact values for degrees such as 30º, 45º, 60º, 90º etc. Having said that, we can think of 105º as 45º + 60º

Here is the equation needed to solve this problem:

cos 105º = [cos (60º + 45º)] = [(cos 60º cos 45º) – (sin 60º sin 45º)]

This will simplify by knowing the following values:

cos 60º = ½

cos 45º = 1/√2

sin 60º = √3/2

sin 45º = 1/√2

Substituting these values we will get [(½ x 1/√2) – (√3/2 x 1/√2)]

Which will simplify to (1-√3)/2√2

Short version : the exact value in radian is (1-√3)/2√2 which is a negative value

Good luck 🙂

5 years ago

cos(105) = cos(60 + 45) = cos 60 cos 45 – sin 60 sin 45 = (1/2)(1 /√2) – ( √3/2)(1/√2) = ( 1 – √3) / 2√2 rationalize the denominator by multiplying top and bottom with √2 = (1/4)(√2 – √6) 2) tan 15 = tan(45 – 30) = tan 45 – tan 30 / (1 + tan 45 tan 30) = ( 1 – 1 /√3) / (1 + 1/√3) = (√3 – 1) / (√3 + 1) rationalize the denominator by multiplying top and bottom with ( √3 – 1) (√3 – 1) (√3 – 1)/ (√3 + 1)(√3 – 1) = (3 + 1 – 2√3) /(3 – 1) = (4 – 2√3) / 2 = 2 – √3

A few days ago

Anonymous

exact value would be a fraction not decimal… i cant really remember the unit circle at the moment since its summer break and i havent had math for like 3 months

buuuuuut im pretty sure its 5pi/4

A few days ago

Anonymous

cos105 = cos (180-75) = – cos75

= -{cos (30+45)} = -{cos30 cos45 – sin30 sin45)

simplify this (dont forget the minus outside)

A few days ago

Ethiebear

-0.258819045

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What is the exact value of cos 105 degrees?

What is the exact value of cos 105 degrees?

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