How do you find two solutions of cos θ = √(2) / 2 in radians?
I need to know for a math worksheet for Pre Calc. If you could tell me how to find with your work shown, that would be very helpful. It would be appreciated if you do not use a calculator. Thank you.
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cosine is positive in the following 2 quadrants
from 0 - π/2 and from 3π/2 to 2π.
For cos θ = √(2) / 2; θ = π/4 and 3π/2-π/4 = 5π/4, so the 2 solutions are π/4 & 5π/4.
θ = 45 deg = pi/4
It's common math knowledge that in a 45 deg right angled triangle
tan(45) = 1
sin(45) = cos(45) = 1/â2 = â2/2
http://i32.tinypic.com/24yaglh.jpg
Other solution is the reflection of the first about the x=Ï
http://i26.tinypic.com/2w4iwi9.jpg