Differentiation to find Max torque and angle it occours

[exodus1]

Torque T = 3sin(2Ө)+6sin(Ө) where Ө is the torque position and 0<=Ө<π
find value of [FONT=arial, sans-serif]Ө for which max torque occurs and the max torque.

[/FONT]i can't seem to simplify the equation to get a value of [FONT=arial, sans-serif]Ө after I have differentiated
i have draw the graph and believe the answer of [/FONT]Ө[FONT=arial, sans-serif] to be about 1.047 making the max T value about [/FONT]

7.7942

 

[wjm11]

Differentiation to find Max torque and angle it occours

Torque T = 3sin(2Ө)+6sin(Ө) where Ө is the torque position and 0<=Ө<π
find value of Ө for which max torque occurs and the max torque.

i can't seem to simplify the equation to get a value of Ө after I have differentiated
i have draw the graph and believe the answer of Ө to be about 1.047 making the max T value about 7.7942

0 = cos(2x) + cosx

cos(2x) = 2cos^2(x) – 1 (Double-Angle Formula)

0 = 2cos^2(x) – 1 + cosx

0 = 2cos^2(x) + cosx – 1 (Quadratic Equation.)

cosx = [-1 +/- (1^2 – 4(2)(-1))^(.5)]/(2(2)) (Quad. Form.)

cosx = [-1 +/- 3]/(4)

cosx = -1 or ½

0 <= x < π (Given.)

cosx = ½

x = pi/3