Use an appropriate Half-Angle Formula to find the exact value of the expression. cos 112.5°?
回答 (8)
2016-04-26 6:18 am
✔ 最佳答案
Since, cos(2*112.5) = cos(225) = cos(180+45) = -cos(45). ................... [1]So,
2cos^2(112.5) -1 = -cos(45) = -1/√2, ==> cos^2(112.5) = -1/2√2 = 0.5/√2,
Or,
cos(112.5) = √[-0.5/√2]. >==================================< ANSWER
2016-04-26 6:10 am
cos²(θ/2) = (1 + cosθ)/2
When θ/2 = 112.5°, θ = 225° :
cos²(112.5°)
= [1 + cos(225°)]/2
= [1 + cos(180° + 45°)]/2
= [1 + (√2)/2]/2
= (2 + √2)/4
As 112.5° is in the second quadrant, cosθ < 0. then :
cos(112.5°) = -[√(2 + √2)]/2
When θ/2 = 112.5°, θ = 225° :
cos²(112.5°)
= [1 + cos(225°)]/2
= [1 + cos(180° + 45°)]/2
= [1 + (√2)/2]/2
= (2 + √2)/4
As 112.5° is in the second quadrant, cosθ < 0. then :
cos(112.5°) = -[√(2 + √2)]/2
2016-11-10 8:01 pm
since, cos(2*112...5) = cos(225) = cos(180+45) = -cos(45)... ......................................................... [1]
so,
2cos^2(112...5) -1 = -cos(45) = -1/√2, ==> cos^2(112...5) = -1/2√2 = 0...5/√2,
or,
cos(112...5) = √[-0...5/√2]... >==================================< answer
so,
2cos^2(112...5) -1 = -cos(45) = -1/√2, ==> cos^2(112...5) = -1/2√2 = 0...5/√2,
or,
cos(112...5) = √[-0...5/√2]... >==================================< answer
2016-09-09 10:21 am
cos²(θ/2) = (1 + cosθ)/2
when θ/2 = 112.........5°, θ = 225° :
cos²(112.........5°)
= [1 + cos(225°)]/2
= [1 + cos(180° + 45°)]/2
= [1 + (√2)/2]/2
= (2 + √2)/4
as 112.........5° is in the second quadrant, cosθ &lt; 0......... then :
cos(112.........5°) = -[√(2 + √2)]/2
when θ/2 = 112.........5°, θ = 225° :
cos²(112.........5°)
= [1 + cos(225°)]/2
= [1 + cos(180° + 45°)]/2
= [1 + (√2)/2]/2
= (2 + √2)/4
as 112.........5° is in the second quadrant, cosθ &lt; 0......... then :
cos(112.........5°) = -[√(2 + √2)]/2
2016-08-25 12:05 am
cos(225) = cos(180 + 45) = -cos(45) = - √2/2
so cos(112...5) = cos(225/2) = -√((1 +cos(225))/2
etc...
so cos(112...5) = cos(225/2) = -√((1 +cos(225))/2
etc...
2016-06-04 7:13 pm
cos(225) = cos(180 + 45) = -cos(45) = - √2/2
so cos(112...5) = cos(225/2) = -√((1 +cos(225))/2
etc...
so cos(112...5) = cos(225/2) = -√((1 +cos(225))/2
etc...
2016-04-26 7:20 am
Okay.
2016-04-26 6:04 am
cos(225) = cos(180 + 45) = -cos(45) = - √2/2
so cos(112.5) = cos(225/2) = -√((1 +cos(225))/2
etc.
so cos(112.5) = cos(225/2) = -√((1 +cos(225))/2
etc.
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