Question

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

Please explain ^_^

Answer 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.

Answer 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
x=1.931688π=6.06858 radians
Check: sin(x) = -0.2129628
tan(x) = -0.2179628
Thus sin(x) and tan(x) agree within 2 significant figures.

Answer 3

If you had to put the answer in radians what would it be?

Answer 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.

Answer 5

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

Answer 6

I guess we should use the first derivative to see the max