Mathematics Dictionary
Dr. K. G. Shih
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Keyword - Sin(30) = 1/2
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Angle = 30 degrees = pi/6 radians. pi = 3.1416
Q1. Prove that sin(30) = 1/2
* Right angle triangle ABC and angle A=30 degrees. C=90 degrees
* Theory : Opposite side of angle A is half of hypothesis.
* Trigonometric ratio : sin(A) = Opp/Hyp
* Hence sin(30) = Opp/Hyp = 1/2
* Sin(30) = 1/2
* Tan(30) = sqr(3)/2
* Cos(30) = sqr(3)/2
* Sin(-30) = -1/2
* Tan(-30) = -sqr(3)/2
* Cos(-30) = +sqr(3)/2
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Q2. Value of Sin(A) related with sin(30)
* Sin(150) = sin(180 - 30) = sin(30) = 1/2
* Sin(210) = sin(180 + 30) =-sin(30) =-1/2
* Sin(330) = sin(360 - 30) =-sin(30) =-1/2
* Sin(390) = sin(360 + 30) = sin(30) = 1/2
* Sin(510) = sin(360 + 150) = sin(150) = 1/2
* Sin(570) = sin(360 + 210) = sin(210) =-1/2
* Sin(690) = sin(360 + 330) =-sin(330) =-1/2
* Sin(750) = sin(720 + 30) = sin(30) = 1/2
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Q3. Why sin(330) is negative ?
* Angle 030 is in 1st quadrant and sin(030) is positive
* Angle 150 is in 2nd quadrant and sin(150) is positive
* Angle 210 is in 3rd quadrant and sin(210) is negative
* Angle 330 is in 4th quadrant and sin(330) is negative
sin(A) = (+) | sin(A) = (+)
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sin(A) = (-) | sin(A) = (-)
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Q4. Solve sin(A) = 1/2
1. Angle A between -360 and 360 Then A=30, 150, -210, -330
2. General solution
* Principal angle A=30 for sin(A)=1/2
* Sin(A) = (+) and A=30 in 1st quadrant and 150 in 2nd quadrant
* Hence A = 360*k + 030 in 1st quadrant
* Hence A = 360*k + 150 in 2nd quadrant
* Answer is A = 2*k*pi + pi/6 and A = (2*k+1)*pi + pi/6
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Remarks
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* The author spent more than 10 years to compile Math Dictionary
* You should have it on your computer
* For more information, Please contact Dr. K. G. Shih
* Visit the URL to get more samples
* Visit the URL to view 130 graphic sample in Program WebABC
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