Using the double angle formula,find cos 120 degrees?
Using the double angle formula, how can we find the value of cos(120 degrees)?
6 Answers
cos 2A = cos^2A - sin^2A
cos 2(60°) = cos^2(60°) - sin^2(60°)
cos 2(60°) = (cos60°)^2 - (sin60°)^2
cos 2(60°) = (1/2)^2 - ((√3)/2)^2
cos 2(60°) = 1/4 - 3/4
cos 2(60°) = -2/4 or -1/2 (Answer)
Hope this helps!
Feb 12, 2025
The formula for cos (α + ß) is cos α cos ß - sin α sin ß. But, if ß = α, then the formula is this:
cos (α + α) = cos 2α = cos α cos α - sin α sin α = cos² α - sin² α.
Let α = 60°. Then 2α = 120°, and by the double angle formula above, this is true:
cos 120° = cos² 60° - sin² 60°.
cos 60° = ½
sin 60° = (√3)/2.
Plugging the cosine and sine of 60° into the formula, we get this:
cos 120° = (½)² - [(√3)/2]²
cos 120° = ¼ - 3/4
cos 120° = (1 - 3)/4
cos 120° = -2/4
cos 120° = -½.
Use your calculator to confirm that cos 120° = -½.
sin 120 = 2 sin 60 cos 60
sin 120 = 2*(1 / 2) sqrt 3 * (1 / 2)
sin 120 = ( 1 / 2) sqrt 3
cos 120 = sqrt [ 1 - sin^2 120 ]
cos 120 = sqrt [ 1 - (3 / 4) ]
cos 120 = sqrt ( 1 / 4)
cos 120 = 1 / 2
cos120deg =cos(60+60) =cos60cos60-sin60sin60 (1/2*1/2)-{(3)^1/2 /2]^2 1/4-3/4 -2/4
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