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Trigonometric Formulas

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					                               Trigonometric Formulas

This is a list of the most common formulas that you should know, not only for the exam,
but just in general as you take calculus and beyond.

1st Quadrant Measures:

        radians   sin     cos     tan
  0        0         0        1        0
 30°       /6     1/ 2      3/2      3 /3
 45°       /4      2/2      2/2      1
 60°       /3      3/2     1/ 2         3
 90°      /2        1       0       N/A

  Also, be able to draw accurate graphs of sin and cos.

Conversions from other quadrants to 1st quadrant:

Q2 to Q1:  - ;      Q3 to Q1:  - ;       Q4 to Q1: 2 - .

If you forget these, draw a circle and use symmetry and common sense.

Signs in other quadrants:




A mnemonic: "All Students Take Calculus". A = all are + in Q1; S = sine is + in Q2; T
= tangent is + in Q3; C = cosine is + in Q4.

Inverse trig functions:

y = sin-1 x: answers will be in Q1 or Q4, use symmetry to get other answers.
y = cos-1 x: answers will be in Q1 or Q2, use symmetry to get other answers.
y = tan-1 x: answers will be in Q1 or Q4, use symmetry to get other answers.

Know the domains and ranges of the inverse trig functions.

                   Know midline, amplitude, period based on graphs!!!
Basic Identities:

          sin x
tan x 
          cos x

sin2 x + cos2 x = 1   (Corollaries: sin2 x = 1 - cos2 x,     cos2 x = 1 - sin2 x)

sin (2x) = 2 sin x cos x

cos (2x) = cos2 x - sin2 x = 2cos2 x - 1 = 1 - 2sin2 x.

                           
sin x    cos x     cos x    sin x       (shift identities)
       2                    2

sin(-x) = -sin(x), tan(-x) = -tan(x)      (sine and tangent are odd functions)

cos(-x) = cos(x)           (cosine is an even function)


Right Triangles:

                                 opp          adj           opp
                       sin         ; cos      ; tan  
                                 hyp          hyp           adj


"Soh-Cah-Toa". Remember, csc x = 1/sin x, sec x = 1/cos x, cot x = 1/tan x.

Use Pythagoras' formula to determine unknown sides in a right triangle.

Law of Cosines: (Used in SAS or SSS triangles)

Lower case a, b, c are always sides, Capital A, B, C are angles. A is opposite a, etc.

c 2  a 2  b2  2ab cosC .      Analogous formulas for a and b.

Law of Sines:

sin A sin B sin C
          
  a     b     c

Make sure you're in the right mode (degree/radian).

				
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