更新1:
Given that theta is an obtuse angle measured in radians and of that sin theta = k,find , in terms of k, an expression for cos theta
Given that theta is an obtuse angle measured in radians and that sin theta = k, in terms of k, an expression for cos theta?
回答 (3)
2020-07-20 8:24 pm
θ is an obtuse angle, i.e. π/2 < θ < π
Hence, sinθ = k > 0 and cosθ < 0
sin²θ + cos²θ = 1
k² + cos²θ = 1
cos²θ = 1 - k²
cosθ = -√(1 - k²)
Hence, sinθ = k > 0 and cosθ < 0
sin²θ + cos²θ = 1
k² + cos²θ = 1
cos²θ = 1 - k²
cosθ = -√(1 - k²)
2020-07-20 8:36 pm
Consider the example sin(30) = sin(150) = 1/2
cos (30) = √(3)/2 but cos(150) = -√(3)/2
Cosines are negative in the second quadrant
In general (cos θ)^2 = 1 – k^2
with positive or negative options for cos θ
The obtuse angle means θ is in the second quadrant
and that means cos θ is the negative quantity
cos θ = -√(1 – k^2)
cos (30) = √(3)/2 but cos(150) = -√(3)/2
Cosines are negative in the second quadrant
In general (cos θ)^2 = 1 – k^2
with positive or negative options for cos θ
The obtuse angle means θ is in the second quadrant
and that means cos θ is the negative quantity
cos θ = -√(1 – k^2)
2020-07-20 8:20 pm
The Pythagorean identity
-sqrt(1 - k^2)
Negative because obtuse
-sqrt(1 - k^2)
Negative because obtuse
收錄日期: 2021-04-18 18:36:16
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https://hk.answers.yahoo.com/question/index?qid=20200720120903AAVzeDO