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Trigonometry > Identity Tan(squared)x+1=Sec(squared)x
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QuickNotes™ 
Identity Tan(squared)x+1=Sec(squared)x
Main formulas:
Remember where the inverse trigonometric functions are defined (their domains), and where there answers lie (their ranges).
- Arcsine is defined for each x between -1 and 1 (inclusive) and produces an answer between − (π/2) and (π/2) (inclusive).
- Arccosine is defined for each x between -1 and 1 (inclusive) and produces an answer between 0 and π (inclusive).
- Arctangent is defined for each x between − ∞ and ∞ (exclusive) and produces an answer between − (π/2) and (π/2) (exclusive).
Example 1:
Find the arcsines of the following common values: − 1, − [√3/2], − [√2/2], − [1/2], 0, [1/2], [√2/2], [√3/2], 1.Example 2:
Identify each of the arcsine, arccosine, and arctangent functions as odd, even, or neither.Example 3:
Find the arccosines of the following common values: − 1, − [√3/2], − [√2/2], − [1/2], 0, [1/2], [√2/2], [√3/2], 1.Example 4:
Find the arctangents of the following common values: − √ 3, − 1, − [√3/3], 0, [√3/3], 1, √3.Example 5:
Find arcsin(sin(− (7π /6))), arccos(cos(4π /3)), and arctan(tan(− (5π /4))).Discussion
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