Trigonometry

Page 1

General solutions of equations involving cosines;

pheta = 360n^o +/- α

pheta = 2npi +/- α

Example 1;

Find the general solution, in degrees, of the equation cos(pheta) = -0.5

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-0.5 = cosine(120^o)

pheta = 360n^o +/- 120^o

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Example 2;

Find the general solution, in degrees, of the equation cos(5pheta) = ((3)^0.5)/2

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((3)^0.5)/2 is the cosine of (30^o)

5pheta = 360n^o +/- 30^o

pheta = 72n^o +/- 6^o

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Page 2

General solutions of equations involving sines;

pheta = 180n^o + (-1)^n * α

pheta = (pi)n + (-1)^n * α

Example 1;

Find the general solution, in degrees, for the equation sin(pheta = ((3)^0.5)/2

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((3)^0.5)/2 = sin(60^o)

pheta = 180n^o + (-1)^n * 60^o

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Example 2;

Find the general solution, in radians, for the equation sin(4pheta) = 0.7

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Sin^-1(0.7) = 0.775397

... 4(pheta) = (pi)n + (-1)^n * 0.775397

pheta = (pi/4)n + (-1)^n * 0.193849

~~ (pi/4)n + (-1)^n (0.194)

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Page 3

General solutions of equations involving tangents;

pheta = 180n^o + α

pheta = (pi)n + α

Example 1;

Find the general solution, in degrees, of the equation tan(4pheta) = -(3)^0.5

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(3)^0.5 = tan(60^o) ===> tan(60^o) = -(3)^0.5

4(pheta) = 180n^o - 60^o

pheta= 45n^o - 15^o

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Example 2;

Find the general solution, in radians, of the equation tan((pi/4) - 3x) = (3)^0.5

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(3)^0.5 = tan (pi/3)

(pi/4 - 3x) = (pi)n + (pi/3)

3x - (pi/4) = -n(pi) - (pi/3)

3x = -n(pi) - (pi/3) + (pi/4)

3x = -n(pi) - (pi/12)

x = -(n/3)pi - (pi/36)

x = ((pi)n/3) - (pi/36)

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