Question

s(t) =sin t + 2cos t
Find a value of t that satisfies the equation

s(t)= (2 + sqrt3)/2

Answer 1

could you explain how you got that?

Answer 2

the unit circle

Answer 3

you have \[\frac{2+\sqrt{3}}{2}=\frac{2}{2}+\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}+\frac{2}{2}=\frac{\sqrt{3}}{2}+2*\frac{1}{2}\]

Answer 4

so when is sint ,sqrt{3}/2
and when is cost, 1/2

Answer 5

oops when t=pi/3 sorry

Answer 6

\[\sin(\frac{\pi}{3})+2*\cos(\frac{\pi}{3})=\frac{\sqrt{3}}{2}+2*\frac{1}{2}=\frac{\sqrt{3}+2}{2}\]

Answer 7

wait, if t = pi/3, then sine of that is simply sqrt3/2

I'm a little bit confused on your follow up questions, though i understand exactly what you did ahha

Answer 8

my follow up questions?

Answer 9

1/2 is the value of cos t, if you apply the inverse to both sides, then t= pi/3, or 60 degrees

Answer 10

and you can get 1/2 since 2cos(t) is the same as 2 *1/2, 1/2 is the ratio, derived from the unit circle.

Answer 11

you just need to see when you have (1/2, sqrt3/2) on the unit circle

Answer 12

yeah, now i finally see it hehe. Thanks, you've helped me yet again!

Answer 13

np