Wednesday, July 14, 2010

TRIGONOMETRY II (Form 4)

1.  We have learned the ratio of Sine, Cosine and Tangent in earlier years (Form 3) based on a right angle triangle. This Rules are of course, basic rules... The angles involve is from 0 to 90.
Note: Rule No.1 (a2 + b2 = c2) is actually derived from the original rule (hyp)2 = (side)2 + (side)2.

2.  But in Trigo II, we are going to study the values of  Sin, Cos and Tan  from 0 to 360. For this, we need to know the ASTC concept.
The ASTC concept will determine the positive or negative values of Sin/Cos/Tan.
eg.1  Sin 150 is positive, Sin 220 is negative, Sin 310 is negative.
eg.2  Cos 150 is negative, cos 220 is negative, cos 310 is positive.
eg.3  Tan 150 is negative, Tan 220 is Positive, Tan 310 is negative.

3.  The graphs of Sin, Cos and Tan will further make you understand....


4. You need to know that the "basic angle" or the "corresponding angle" is important to determine the values of an angle.
eg 1:  Sin 130 = sin (180 - 130) = + sin 50 = + 0.7660
eg 2:  Sin 230 = sin (230 - 180) = - sin 50 = - 0.7760
eg 3:  Sin 310 = sin (360 - 310) = - sin 50 = - 0.7660

Therefore if sin x = -0.7660,  x = 230 or 310

Similarly, if Cos x = - 0.7660,  x = (180 - 40) = 140  or  (180+40) = 220
And, if Tan x = 1.732, then x = 60  or  240 (180+60).
Therefore, if Tan x = -1.732, then x = 120  or  300.

That's all... Have a nice day..

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