Wolfram Language Fast Introduction for Math Students
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Trigonometry

For basic trig functions, use standard abbreviations (with the first letter capitalized):

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Sin[x]/Cos[x] == Tan[x]
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Add “Arc” for the inverses:

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ArcTan[1]
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Use Pi when working with radian expressions:

(Type ESCpiESC for the π character.)
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Sin[\[Pi]/2]
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Or type ESCdegESC for the built-in Degree symbol:

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Sin[90 \[Degree]]
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Automatically expand (or reduce) trig expressions using identities:

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TrigExpand[Sin[2 x]]
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Factor trig polynomials:

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TrigFactor[Cos[x]^2 - Sin[x]^2]
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Functions like Solve work as well:

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Solve[Cos[x]^2 + Sin[x]^2 == x]
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Specify a domain for solutions:

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Solve[{Tan[x] == 1, 0 < x < 2 Pi}]
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QUICK REFERENCE: Trigonometric Functions »