# math

Find the largest angle for which sine and tangent agree to within two significant figures.

1. so we want
tanx = sinx
sinx/cosx = sinx
cosx = 1
x = 0º, 360º, 720º, ...
As you can see there is no such "largest" angle, they agree (are equal ?) at every multiple of 360º

BTW, then value of the "agreement" would be 0,
i.e. sin360=0, tan360=0
sin 720 = 0, tan 720 = 0 etc.

posted by Reiny
2. The answer is indefinite, since both tangent and sin are cyclic functions.

If we look for the largest angle between 0 and 2π, then we set
sin(x)-tan(x) = 0.005 (for two significant digits)
Solving for x, we get
Check: sin(x) = -0.2129628
tan(x) = -0.2179628
Thus sin(x) and tan(x) agree within 2 significant figures.

posted by MathMate

posted by jojo
4. mmmhhh, looks like MathMate and I took a different interpretation.

I think I read is as if there had been a comma after 'agree', ie

Find the largest angle for which sine and tangent agree, to within two significant figures.

posted by Reiny
5. I think that is how the question is suppose to be interpreted Reiny. Very confusing wording.

posted by jojo
6. I guess we should use the first derivative to see the max

posted by Engineer R

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