"Use the unit circle to find the value of cot(40°)"
I know I can just enter this into a calculator, but when they say "use the unit circle", do they want me to find an exact value? And if so, how would I do that?
I know I can just enter this into a calculator, but when they say "use the unit circle", do they want me to find an exact value? And if so, how would I do that?
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Θ = 40
Radius, r = 1
x = r Cos Θ
x = (1) Cos Θ
x = Cos 40
x = 0.766
y = r Sin Θ
y = (1) Sin Θ
y = Sin 40
y = 0.6428
Tan Θ = y / x
Tan Θ = 0.6428 / 0.766
Tan Θ = 0.8392
Cot Θ = 1 / Tan
Cot Θ = 1 / 0.8392
Cot Θ = 1.1917
¯¯¯¯¯¯¯¯¯¯¯¯¯
Radius, r = 1
x = r Cos Θ
x = (1) Cos Θ
x = Cos 40
x = 0.766
y = r Sin Θ
y = (1) Sin Θ
y = Sin 40
y = 0.6428
Tan Θ = y / x
Tan Θ = 0.6428 / 0.766
Tan Θ = 0.8392
Cot Θ = 1 / Tan
Cot Θ = 1 / 0.8392
Cot Θ = 1.1917
¯¯¯¯¯¯¯¯¯¯¯¯¯
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Exact value can not be written in algebraical form (e.g. using powers, roots, +, -, *, /) so you should just find inexact value. Graph unit circle, x-axis, line x = 1 and choose P on the line x = 1 such that angle xOP = 40 degrees
Then cot(40 degrees) = x-coordinate of P (in units equaled to circle's radius). You just measure it with rule and divide it to radius of the unit circle
Then cot(40 degrees) = x-coordinate of P (in units equaled to circle's radius). You just measure it with rule and divide it to radius of the unit circle