Working out trig without a calculator?

[flibbage0]

I know this might sound really stupid and easy but how do I work out Sin 60 without using a calculator?

Is it just Sin (45+15) and then I'm supposed to know what Sin 45 and Sin 15 are?

Thanks.

 

[Orford]

Some awesome psot on this forum today, may have to start a topic of the day compatition.

Although this may no be as random as I first thought. It has been asked before.

http://www.gamedev.net/topic/571390...-without-a-calculator-does-this-answer-exist/

extract............

Just by looking at wikipedia we can find the trigonometric functions page that says:


Quote:


Prior to computers, people typically evaluated trigonometric functions by interpolating from a detailed table of their values, calculated to many significant figures. Such tables have been available for as long as trigonometric functions have been described (see History below), and were typically generated by repeated application of the half-angle and angle-addition identities starting from a known value (such as sin(π/2) = 1).



Then, following a "see also" link to the Generating trigonometric tables pages we can find the method used to create the tables that rip-off used in high school as well as some faster approximations.

I assume that Wolfram's MathWorld also explains all this, but I didn't bother to look there.

 

[PhilthyPhil]

Sine is the ratio of opp to hyp. So if you take a 30-60-90 triangle you can see sin(60)=½√3

 

[D.P.]

As above, before calculators really existed you would use a trig look-up table and interpolate between values. You can also use above method using triangles

 

[flibbage0]

Sine is the ratio of opp to hyp. So if you take a 30-60-90 triangle you can see sin(60)=½√3

How do I do that, so I have a triangle with 3 angles but don't know what any of the side lengths are

 

[PhilthyPhil]

if you take an equilateral triangle with sides 2-2-2 and split it in half you get a 30-60-90 triangle. Obviously you know one side is 1 and another is 2. You can use pythagoras to find the other is √3

 

[flibbage0]

if you take an equilateral triangle with sides 2-2-2 and split it in half you get a 30-60-90 triangle. Obviously you know one side is 1 and another is 2. You can use pythagoras to find the other is √3

I see, thank you very much

So I am supposed to remember that then.

 

[Tephnos]

I see, thank you very much

So I am supposed to remember that then.

Yeah, the two special triangles is something you wanna remember. (One does 30/60, the other 45)

 

[Srengam]

If your at a level where you need to know this then you should probably be using radians really instead of degrees.

60 degrees is pi/3 radians.

So what your asking is whats sin(pi/3), which is (as mentioned above) is (root 3)/2.

These are things that you don't need to work out eventually, they come up so often that it's second nature.

 

[craarc]

calculator !!!! wtf when i was at school we had to use log tables ...

 

[King Damager]

Sin60 is a relatively easy one to do off the top of your head

Special triangle as others have said. Don't worry though, I never bothered learning them, did fine

kd