Hi,

I have heard its possible to find the sine and cosine of some common angles without calculator.

Can anyone explain how please?

eg.

cos pi/4 = 1/√2

sin pi/4 = 1/√2

cos 5pi/4 = -1/√2

cos pi/3 = 1/2

sin pi/3 = √3/2

Thanks in advance

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- Nov 1st 2012, 05:53 AMScorpFireFinding the sine, cos of common angles without calculator
Hi,

I have heard its possible to find the sine and cosine of some common angles without calculator.

Can anyone explain how please?

eg.

cos pi/4 = 1/√2

sin pi/4 = 1/√2

cos 5pi/4 = -1/√2

cos pi/3 = 1/2

sin pi/3 = √3/2

Thanks in advance - Nov 1st 2012, 06:29 AMBobPRe: Finding the sine, cos of common angles without calculator
Look at the thread

**when tanx = 1** - Nov 1st 2012, 07:06 AMSorobanRe: Finding the sine, cos of common angles without calculator
Hello, ScorpFire!

Quote:

I have heard its possible to find the sine and cosine of some common angles without calculator.

Can anyone explain how please?

For example: .

, consider an isosceles right triangle.

Code:`*`

* *

* * h

1 * *

* *

* 45 *

* * * * *

1

Pythagorus says the hypotenuse is

We have: .

And you can write the trig values of

Memorize "one, one, square-root-of-two".

, consider an equilateral triangle

. . with side length 2. .Draw an altitude.

Code:`*`

*|*

* | *

2 * |y *

* | *

* 60 | *

* * * * *

: 1 : 1 :

Pythagorus says:

And you can write the trig values for

For , turn the above right triangle on its side.

Code:`*`

2 * *

* * 1

* 30 *

* * *_ * *

√3

And you can write the trig values for

For both diagrams, memorize "one, two, square-root-of-three".

Be careful! .Remember that:

. . The shortest side, 1, is opposite the smallest angle, 30^{o}.

. . The longest side, 2, is opposite the largest angle, 90^{o}.

- Nov 1st 2012, 07:50 AMrichard1234Re: Finding the sine, cos of common angles without calculator
Take a point on the unit circle. The cosine of the corresponding angle is simply the x-coordinate (adjacent over hypotenuse). The sine of that angle is the y-coordinate. That's how I usually find sine/cosine in my head by just visualizing the unit circle.

- Nov 2nd 2012, 10:14 PMSalahuddin559Re: Finding the sine, cos of common angles without calculator
There are formulae for finding sin(A+B) and cos(A+B) etc... using these one can extend the values for other angles. For example, sin2A = 2sinAcosA, using which one can find sin(15 degrees) = sqrt(2 - sqrt(3))/2.

Salahuddin

Maths online