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| Math Central | Quandaries & Queries |
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Question from Alisha, a student: If csc theta = 3 and sec theta = square root of 3, what are the values of tan theta and cos^2 theta? |
Alisha,
csc(θ) = 1/sin(θ) and sec(θ) = 1/cos(θ) and hence you have sin(θ) = 1/3 and cos(θ) = 1/√3. Thus
sin2(θ) + cos2(θ) = (1/3)2 + (1/√3)2 = 1/9 + 1/3 = 4/9.
But for any angle θ, sin2(θ) + cos2(θ) = 1. Hence there is no angle θ such that csc(θ) = 3 and sec(θ) = √3.
A better question would be
If csc(θ) = √3 and sec(θ) = √3/√2 what are the values of tan(θ) and cos2(θ)?
Harley
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