HEy, my roommate is needing some help with her class, the section she is doing is trig equations and her problem is sin teta/2 = -sqrt3/2 any help is appreciated.
2007-03-22 19:22:26 · 5 answers · asked by Kacey L 1 in Science & Mathematics ➔ Mathematics
Assume Ø/2 is measured in degrees.
- √3 / 2 indicates that (Ø/2) is in 3rd and 4th quadrants.
(Ø/2) = (180 + 60)°,(360 - 60)°
(Ø/2) = 240°,300°
Ø = 480°,600°
2007-03-22 20:55:03 · answer #1 · answered by Como 7 · 0⤊ 0⤋
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2016-10-19 09:53:38 · answer #2 · answered by olis 4 · 0⤊ 0⤋
Solve sin(theta/2) = -sqrt(3)/2
Sine is negative in the 3rd and 4th quadrant so
pi <= theta/2 <= 2pi (180o <= theta/2 <= 360o)
Note sin(x) = sqrt(3)/2 thus x=pi/3 (60o). Hence
theta/2 = 4pi/3 or 5pi/3 (240o or 300o)
Therefore theta = 8pi/3 or 10pi/3 (480o or 600o)
Answer in radians with degrees in brackets
2007-03-22 19:34:37 · answer #3 · answered by Anonymous · 0⤊ 0⤋
sin (theta / 2) = -sqrt3/2
theta / 2 = arcsin -sqrt/2
theta / 2 = 4pi/3 and 5 pi/3
theta = 8pi/3 and 10 pi / 3
assuming theta is between 0 and 2 pi
2007-03-22 19:28:47 · answer #4 · answered by yup5 2 · 0⤊ 0⤋
sin teta/2=sqrt3/2
i.e. sin teta/2=sin pie/3
i.e. teta/2=pie/3
i.e. teta=2pie/3 is the answer.
2007-03-22 19:39:33 · answer #5 · answered by Anonymous · 0⤊ 0⤋