I need help solving this equation: 3 sin &#x2061;<!-- ⁡ --> ( x ) 3 </msup>

varitero5w

varitero5w

Answered question

2022-06-14

I need help solving this equation:
3 sin ( x ) 3 5 sin ( x ) cos ( x ) + 2 cos ( x ) 2 = 0

Answer & Explanation

Anika Stevenson

Anika Stevenson

Beginner2022-06-15Added 19 answers

it looks like
(1) 3 sin 3 t 5 sin t cos t + 2 cos 2 t = 0
has four solutions in the closed interval [ 0 , 2 π ] . one way to see this is to see (1) as a quadratic equation in x with the change of variables x cos t , y = sin t . we now have
2 x 2 5 y x + 3 y 3 = 0  and  x 2 + y 2 = 1.
draw the graphs of
x = 5 y ± 25 y 2 24 y 3 4  and  x = ± 1 y 2 .

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