How do you solve $cosx (2sinx + 1) = 0$ ?

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Answer 1 · 2015-07-21T04:20:30

Solve: cos x(2sin x + 1) = 0

cos x(2sin x + 1) = 0
a. cos x = 0 --> $x = pi/2 and x = 3pi/2$

b. $sin x = - 1/2$ . Trig table gives:
$x = - pi/6$ or $(11pi)/6$ .
Trig unit circle gives another arc $x = (7pi)/6$ that has same sine value.

Finally, within interval $(0, 2pi)$ , there are 4 answers:
$pi/2$ ; $(7pi)/6$ , $(3pi)/2$ ; and $(11pi)/6.$

How do you solve cosx (2sinx + 1) = 0cosx (2sinx + 1) = 0?