TRIGONOMETRY: how would I go about solving this
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TRIGONOMETRY: how would I go about solving this

[From: ] [author: ] [Date: 11-12-27] [Hit: ]
x = 0.y = 0.Tan Θ = 0.6428 / 0.Tan Θ = 0.Cot Θ = 1 / 0.......
"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?

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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
¯¯¯¯¯¯¯¯¯¯¯¯¯

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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
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