SOLUTION: give answers in degrees if sin2 theta+cos theta=0 I am not sure how to start this problem other than sin2 theta would be (2sin theta cos theta)

Question 470370: give answers in degrees if
sin2 theta+cos theta=0
I am not sure how to start this problem other than sin2 theta would be
(2sin theta cos theta)
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
give answers in degrees if
sin2 theta+cos theta=0
====================================
You already recognized that you need to use the trig identity sin(2 theta)=2sin(theta)cos(theta)
Substituting that expression gives (and letting theta = x to make it easier to write):
2sin(x)cos(x)+cos(x)=0
cos(x)(2sin(x)+1)=0
This equation is satisfied if either of the two factors are equal to 0.
So we have
cos(x) = 0
2sin(x)+1 = 0
Restricting ourselves to the interval (0,360 deg) the two solutions are
x = 90 deg
sin(x) = -1/2
x = 210 deg
RELATED QUESTIONS
HELLO I am having troubles with the following: if cos(theta) = -1/3 and theta is in (answered by lwsshak3)

how would i verify the identity: 2sin cubed theta cos theta+2sin theta cos cubed theta=... (answered by stanbon)

I am having a problem with this question...please don't just give me the answer, I would... (answered by drk,jim_thompson5910)

I am not sure where to start or how to do this problem! If 0 (answered by Alan3354)
Find the solution of sin2(theta)=cos(theta) if 0 deg. <= (theta) < 180... (answered by Alan3354)
cos theta=3/5, while 3pi/2 < theta < 2pi what is sin 2theta? I know that the equation is... (answered by Fombitz)
9 cos^2 theta + 3 cos theta =0, where 90 degrees < theta < 180 degrees, what is the value (answered by scott8148)
I have 2 questions" 1)Find all values of θ that satisfy the equation over the... (answered by rothauserc)
if theta is in Quadrant II and cos theta = -3/4 , find an exact value for sin2... (answered by lwsshak3)