Remembering sin and cos values

NIH · 2005-06-19 04:00:21

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

MathsIsFun · 2005-06-19 09:45:30

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.

katecaroline · 2005-06-21 03:36:49

All I can say is God bless the calculator.

Roraborealis · 2005-06-21 03:54:01

Indeed, I have learnt today to be grateful for a calculator thanks to you lot.

I love pi · 2005-06-30 22:39:45

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

MathsIsFun · 2005-06-30 22:53:13

Hi Pi!

Jaz2 · 2005-07-04 22:50:39

Hi its Jaz2 im new here do u know key or jaz1????????

MathsIsFun · 2005-07-04 22:54:04

Only a little ...

Jai Ganesh · 2005-07-04 23:12:09

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)

phoenix86 · 2005-08-08 17:51:46

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

Jai Ganesh · 2005-08-09 00:08:29

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 Jai Ganesh (2005-08-09 00:09:30)

mathsyperson · 2005-08-09 00:12:34

I use CAST. It's quicker as long as you remember that it starts in the 4th quadrant.

wcy · 2005-08-15 00:48:41

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

John E. Franklin · 2005-08-30 13:33:53

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.

ahgua · 2005-08-30 15:55:03

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)

Monox D. I-Fly · 2019-11-06 18:45:16

ganesh wrote:

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 square root of 2 has mnemonic??? What is it???

Math Is Fun Forum

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

Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

#11 2005-08-09 00:08:29

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

#13 2005-08-15 00:48:41

Re: Remembering sin and cos values

#14 2005-08-30 13:33:53

Re: Remembering sin and cos values

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

Re: Remembering sin and cos values

#16 2019-11-06 18:45:16

Re: Remembering sin and cos values

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