can someone explain this to me:
tan(theta) = 60/x
x = 60/tan(theta)
x = 60cot(theta)
i dont understand how the tangent switches to cotangent.
Cotangent is just 1 over tangent so
In the same way that cosecant is 1 over sine, and secant is 1 over cosine.
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So your intitial equation is:
then multiply both sides by
Simplify (cancel out tangents on LHS and x's on RHS) to get your second equation.
You can partition the RHS like so:
And you see that on the RHS 1/tangent = cotangent so
Which is your last equation.
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Some other things to note:
since you can multiply both sides by tangent over cotangent and get
and also since
it follows that
so