How to evaluate values of sinx cosx tanx for very large values of x?

[Qwertyuiop[]]

Hi, how can we evaluate the values of trig function when the angle is HUGE, like say for example tan(2131pi/6), or sin(10201pi/5)?

 

[blamocur]

Hi, how can we evaluate the values of trig function when the angle is HUGE, like say for example tan(2131pi/6), or sin(10201pi/5)?

Use the fact that all trig functions have period of [imath]2\pi[/imath].

 

[Dr.Peterson]

Hi, how can we evaluate the values of trig function when the angle is HUGE, like say for example tan(2131pi/6), or sin(10201pi/5)?

Subtract an appropriate multiple of the period of the function, to bring it within 0 to 2 pi.

For example, since the period of the tangent is pi, and 2131/6 = 355 1/6, subtract 355 pi from the angle.

 

[Qwertyuiop[]]

Subtract an appropriate multiple of the period of the function, to bring it within 0 to 2 pi.

For example, since the period of the tangent is pi, and 2131/6 = 355 1/6, subtract 355 pi from the angle.

I forgot to mention that we are not allowed to use calculators so I have to use long division in case the fraction cannot be simplified?

 

[khansaheb]

I have to use long division in case the fraction cannot be simplified?

And that's how most of us did it !!! It builds character......

 

[BigBeachBanana]

I forgot to mention that we are not allowed to use calculators so I have to use long division in case the fraction cannot be simplified?

Learn divisibility rules.

For example,
If a number ends in 0 or 5 it's divible by 5, so I can rewrite 10201 = 10200 + 1.

Therefore sin(10201pi/5) = sin(pi/5)

 

[khansaheb]

Hi, how can we evaluate the values of trig function when the angle is HUGE, like say for example tan(2131pi/6), or sin(10201pi/5)?

Other than some very specific values, you cannot get "rational" numbers for trigonometric functions - and you will be hard-pressed to manipulate further w/o calculators. For example,

sin(10201 π/5) = sin(π/5) = 0.587785 (from calculator)

On the other hand if the problem is to evaluate:

sin(10201 π/5) - sin(π/5) = 0 .............you should not need a calculator

or

sin(10201 π/5) ÷ sin(π/5) = 1 .............you should not need a calculator

It depends on the FIND of the problem.