QUADRANTs
With unit circle, there are more benefits, to find trig values of angle over 90 degrees. What will sin135º be? Can you guess?
Think.
Okay. Here is the image. There is an angle Θ on the second quadrant. Let's compare with one on the first quadrant. We know that cosine value is x value, sine value is y value, and tangent value is y/x, which is the slope of hypothenus.
First, x value. When you say the x value of triangle on the first quadrant is x, how can you call the x value on the second quadrant? It reflects about the y axis, so only the sign changes. -x (nevative)!
Y value? First and second quadrant has same y value, so stay same.
Tangent, it is reflecting about the y axis, so it also changes the sign.
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1st 2nd
cos x -x
sin y y
tan y/x -y/x
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Now, the angle is on the third quadrant. What happen to x value? Negative. What about y value? also negative. What about the slope of hypothenus? Stay same.
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1st 2nd
cos x -x
sin y -y
tan y/x y/x
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Lastly, 4th quadrants. What happen to x value on fourth quadrant? It stays same. Y value is opposite, changing the sign, and the sign of slope also changes.
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1st 2nd
cos x x
sin y -y
tan y/x -y/x
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Okay. When you just read descriptions, you think you get it, but when you are asked to answer 'what is sin225º?', you will be just, blank. So, many teachers give you the way to memorize, and it is quite benefitial. However, understand first and memorize. Understanding is the very first thing. Also, when you understand, it is much easier to memorize.
Okay, when you see the pattern, you can find that except first quadrant, other three have only one positive value, sine for 2nd Q, tangent for 3rd Q, and cosine for 4th Q, and all three on 1st Q.
1st, All, 2nd, Sin, 3rd, Tan, and 4th, Cos. A.S.T.C. There is some sentences might help you. All Students Take Calculus. This sentence doens't have any meaning, but just to memorize these four letters. A.S.T.C.
Got it? Got it!
Only one little point more.
You can see that all angles is the angle that the hypotenus and x-axis make. Not y-axis. Therefore, when the angle is on 2nd quadrant,
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