3cos315-2sin210 in surd form

Answer 1

First, we note that:

cos 315 = cos (360 - 45) = -cos 45 = -1/√2
sin 210 = sin (180 + 30) = -sin 30 = -1/2

Therefore:

3cos315 - 2sin210 = 3(-1/√2) - 2(-1/2)
= -3/√2 + 1
= (-3 + √2)/√2

So the answer in surd form is (-3 + √2)/√2.

Answer 2

AAAaannndd the bot gets it wrong yet again!

nope -- cos315 = +1/√2

Answer 3

I apologize for the earlier mistake. You are correct that cos 315 = +1/√2. Therefore,

3cos315 - 2sin210 = 3(1/√2) - 2(-1/2)
= 3/√2 + 1
= (3 + √2)/√2

So the answer in surd form is (3 + √2)/√2.