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#1 2005-06-20 02:00:21
- NIH
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Remembering sin and cos values
If you have trouble remembering the values for sin and cos of 0°, 30°, 45°, 60°, and 90°, the following device may help. This looks better when written out as a horizontal table, but I'll write it vertically here...
sin 0° = sqrt(0)/2
sin 30° = sqrt(1)/2
sin 45° = sqrt(2)/2
sin 60° = sqrt(3)/2
sin 90° = sqrt(4)/2
cos 0° = sqrt(4)/2
cos 30° = sqrt(3)/2
cos 45° = sqrt(2)/2
cos 60° = sqrt(1)/2
cos 90° = sqrt(0)/2
2 + 2 = 5, for large values of 2.
#2 2005-06-20 07:45:30
- MathsIsFun
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Re: Remembering sin and cos values
That is just TOO neat. I had never thought of it like that.
Now, how do I rememver that sin 0° = 0 and cos 0° = 1 ? It is like trying to remember port and starboard !
Just kidding ... I have no trouble at all remembering port. 
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#3 2005-06-22 01:36:49
- katecaroline
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Re: Remembering sin and cos values
All I can say is God bless the calculator.
» I always knew that looking back on the tears would make me laugh,
but I never knew looking back on the laughs would make me cry. «
<3
#4 2005-06-22 01:54:01
- Roraborealis
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Re: Remembering sin and cos values
Indeed, I have learnt today to be grateful for a calculator thanks to you lot.
School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?
#5 2005-07-01 20:39:45
- I love pi
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Re: Remembering sin and cos values
Oh my, u are an intelligent bunch of beings! i don't think i'll ever be able to memorise the sin values, even with your uber neat device
#6 2005-07-01 20:53:13
- MathsIsFun
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Re: Remembering sin and cos values
Hi Pi!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#7 2005-07-05 20:50:39
- Jaz2
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Re: Remembering sin and cos values
Hi its Jaz2 im new here do u know key or jaz1????????
x x x x Jaz x x x x
#8 2005-07-05 20:54:04
- MathsIsFun
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Re: Remembering sin and cos values
Only a little ...
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#9 2005-07-05 21:12:09
- ganesh
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Re: Remembering sin and cos values
Similalry, how do you tell whether sin or cos or tan of an angle is positive or negative?
Just remember the mnemonic 'All Silver Tea Cups'.
In the first quadrant, i.e. 0 to 90 degrees, All the angles are positive.
In the second quadrant, 90-180 degrees, only Sine is positive (remember S of Silver!)
In the third quadrant, 180-270 degrees, only Tan is positive. (remember T for Tea)
In the fourth quadrant, i.e. 270 to 360 degrees, only Cos is positive. (C for Cups)
Character is who you are when no one is looking.
#10 2005-08-09 15:51:46
- phoenix86
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Re: Remembering sin and cos values
NIH ...... you saved me countless hours trying to guess the values with my calculator... THANKS !! 
#11 2005-08-09 21:15:22
- kylekatarn
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Re: Remembering sin and cos values
I think mnemonics is a disrespect to math. Math is subjects should be understood, not memorized like a song..
but that's my opinion.
#12 2005-08-09 22:08:29
- ganesh
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Re: Remembering sin and cos values
kylekatarn wrote:
I think mnemonics is a disrespect to math.
You are right, but sometimes, it is important to remember things. We all know that the square root of 2 can be calculated when required, but remembering 1.4142 helps when we are required to solve problems quickly. The mnemonic 'All Silver Ta Cups' was for the benefit of students who may need to know whether Cosθ or Sinθ or Tanθ is positve or negative for a certain value of θ while solving problems, when time is crucial.
Last edited by ganesh (2005-08-09 22:09:30)
Character is who you are when no one is looking.
#13 2005-08-09 22:12:34
- mathsyperson
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Re: Remembering sin and cos values
I use CAST. It's quicker as long as you remember that it starts in the 4th quadrant.
Why did the vector cross the road?
It wanted to be normal.
#14 2005-08-15 22:48:41
- wcy
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Re: Remembering sin and cos values
another way of remembering sin/cos 45 and sin/cos 60 or 30 is to draw some triangles.
For 45 degrees, draw an isosceles right angled triangle, with sides 1,1,√2
For 60 degrees, draw an equilateral triangle with sides 2 by 2 by 2 and divide it into 2 equal triangles by bisecting one of the 60 degree angles
for sin 0, cos 0, just imagine a triangle with an angle so small that it is almost 0
#15 2005-08-31 11:33:53
- John E. Franklin
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Re: Remembering sin and cos values
I associate cosine with the x-axis so cosine it is positive in 1st and 4th quadrants.
I associate sine with the y-axis so it is positive in the 1st and 2nd quadrants.
Since tangent is rise over run, or slope, or the derivative of a curve (the tangent of the curve),
then the tangent is positive in 1st and 3rd quadrants.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#16 2005-08-31 13:55:03
- ahgua
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Re: Remembering sin and cos values
To remember the trigo ratio:
1. Draw a table
Trigo/Angle 30 45 60
sin 1 2 3 [write 1,2,3 in the first row(sin)]
cos 3 2 1 [reverse the order of values]
tan 3 1 3 [write 3,1,3 in the third row(tan)]
2. Square root every no. in the table
Trigo/Angle 30 45 60
sin 1 √2 √3
cos √3 √2 1
tan √3 1 √3
*** √1 = 1. So, need not square root 1!
3. Divide value in first 2 rows by 2
Trigo/Angle 30 45 60
sin 1/2 √2 /2 √3 /2
cos √3 /2 √2 /2 1 /2
tan √3 1 √3
4. Reciprocate the first value in the tan row.
Trigo/Angle 30 45 60
sin 1/2 √2 /2 √3 /2
cos √3 /2 √2 /2 1 /2
tan 1/ √3 1 √3
Easy right.
For angle of 0°, 90°, 180°, 270° and 360°
1. Draw a table.
Start with the sin row: write 0 and 1, alternating each value, starting with 0
SO:
0 90 180 270 360
sin 0 1 0 1 0
cos
tan
2. Reverse the order of value of cos with reference to sin
0 90 180 270 360
sin 0 1 0 1 0
cos 1 0 1 0 1
tan
3. Copy down the value for tan with reference to sin, substituting all "1"s with undefined "∞"s
SO:
0 90 180 270 360
sin 0 1 0 1 0
cos 1 0 1 0 1
tan 0 ∞ 0 ∞ 0
4. Make the second "1" negative for the first and second row
SO:
0 90 180 270 360
sin 0 1 0 -1 0
cos 1 0 -1 0 1
tan 0 ∞ 0 ∞ 0
That's all
Last edited by ahgua (2005-08-31 13:57:21)
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