SOLUTION: Solve this equation for 0 ≤ θ ≤ 2 : sin θ cos θ + cos θ = 0. a. π/2, 3π/2 b.0, π c.π/2, -1

Algebra ->  Finance -> SOLUTION: Solve this equation for 0 ≤ θ ≤ 2 : sin θ cos θ + cos θ = 0. a. π/2, 3π/2 b.0, π c.π/2, -1      Log On


   

Question 1087691: Solve this equation for 0 ≤ θ ≤ 2 : sin θ cos θ + cos θ = 0.
a. π/2, 3π/2
b.0, π
c.π/2, -1
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure the domain of theta is limited to +0%3C=+theta+%3C=+2+ ? (It looks as though it might really be +0+%3C=+theta+%3C=+2pi+ (?) )
I ask because for +0%3C=theta%3C=2+ none of the answers work because they all have values of +theta outside [0,2].
—
If the domain is +0+%3C=+theta+%3C=+2pi+ then (a) works.
First lets factor out a +cos%28theta%29+
+sin%28theta%29cos%28theta%29+%2B+cos%28theta%29+
= +cos%28theta%29%28sin%28theta%29%2B1%29+=+0+ (*)
(*) is zero if cos%28theta%29+=+0 or +sin%28theta%29%2B1+=+0+
—
(a)
+cos%28pi%2F2%29+=+0+ so (*) is zero
+cos%283pi%2F2%29+=+0 so again (*) goes to zero.
—
(b) does not work because (*) is not zero for +theta+=+0+ or +theta+=+pi+
(c) does not work because (*) is not zero for +theta+=+-1+ ( it is zero only for +theta+=+pi%2F2+ )