Evaluate without a calculator: 3 sin^2 45 - cos 120?

Answer 1

sin 45 = sqrt(2)/2, so (sin 45)^2 = 2/4 = 1/2

for 120 degrees, the reference angle is 60 and it's in the 2nd quadrant, where cos is negative, so

cos 120 = -cos 60 = -1/2

So the answer is 3(1/2) - (-1/2) = 3/2 + 1/2 = 4/2 = 2.

Answer 2

Look at a right triangle with a 45 degree angle and hypotenuse length = 1. The other angle is 45 degrees. It is an isosceles triangle! Use the pythagorean theorem: a^2 + a^2 = 1 2 a^2 = 1 a^2 = 1/2 a = sqrt(1/2) No memorization necessary ;-)

Answer 3

sin"2 45 is 0.5, and cos 120 is -0.5. So the result is 1.

Answer 4

3sin^2 45=3(1/rt2)^2=3/2
cos120*=cos(180-60)
=-cos60*
=-1/2
so the answer=3/2-(-1/2)=2