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Secant and Cosecant Functions

Main definitions and formulas:

• The tangent function is defined by
  

  tanθ = sinθ cosθ

  for values of θ where cosθ ≠ 0. (For values of θ where cosθ = 0, the tangent is undefined.)
• The cotangent function is defined by
  

  cotθ = cosθ sinθ

  for values of θ where sinθ ≠ 0. (For values of θ where sinθ = 0, the cotangent is undefined.)
• Master formula for right triangles: SOHCAHTOA!
  

  sinθ = opposite side hypotenuse     cosθ = adjacent side hypotenuse     tanθ = opposite side adjacent side

• Degrees Radians Cosine Sine Tangent Cotangent 0 0 1 0 0 undefined 30 π 6 √ 3 2 1 2 √ 3 3 √ 3 45 π 4 √ 2 2 √ 2 2 1 1 60 π 3 1 2 √ 3 2 √ 3 √ 3 3 90 π 2 0 1 undefined 0

• The slope of a line is the tangent of the angle that the line makes with the x-axis.
• Use these values to find sines and cosines in other quadrants. The mnemonic ASTC (All Students Take Calculus) helps you remember which ones are positive in which quadrant. (All, Sine, Tangent, Cosine)