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#1 2005-06-19 04:00:21

NIH
Member
Registered: 2005-06-14
Posts: 33

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.

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#2 2005-06-19 09:45:30

MathsIsFun
Registered: 2005-01-21
Posts: 7,691

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

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#3 2005-06-21 03:36:49

katecaroline
Member
Registered: 2005-06-19
Posts: 35

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

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#4 2005-06-21 03:54:01

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

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?

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#5 2005-06-30 22:39:45

I love pi
Member
Registered: 2005-06-30
Posts: 11

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

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#6 2005-06-30 22:53:13

MathsIsFun
Registered: 2005-01-21
Posts: 7,691

Re: Remembering sin and cos values

Hi Pi!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2005-07-04 22:50:39

Jaz2
Member
Registered: 2005-07-04
Posts: 80

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

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#8 2005-07-04 22:54:04

MathsIsFun
Registered: 2005-01-21
Posts: 7,691

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

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#9 2005-07-04 23:12:09

ganesh
Registered: 2005-06-28
Posts: 28,275

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)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#10 2005-08-08 17:51:46

phoenix86
Member
Registered: 2005-08-08
Posts: 1

Re: Remembering sin and cos values

NIH ...... you saved me countless hours trying to guess the values with my calculator... THANKS !!

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#11 2005-08-08 23:15:22

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

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.

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#12 2005-08-09 00:08:29

ganesh
Registered: 2005-06-28
Posts: 28,275

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 00:09:30)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#13 2005-08-09 00:12:34

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

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.

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#14 2005-08-15 00:48:41

wcy
Member
Registered: 2005-08-04
Posts: 117

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

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#15 2005-08-30 13:33:53

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

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

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#16 2005-08-30 15:55:03

ahgua
Member
Registered: 2005-08-24
Posts: 25

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 (2005-08-30 15:57:21)

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

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