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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. smile


"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 wink
 

#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 !! big_smile

 

#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.  smile

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.


igloo myrtilles fourmis
 

#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 smile

Last edited by ahgua (2005-08-31 13:57:21)


Life is a passing dream, but the death that follows is eternal...
 

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