if sin teta = -1/3 and teta does not lie in the quadrant 3 find the value of cos teta

Question

FIND THE VALUE OF COS TETA

Answer 1

DO YOU REMEMBER THAT THE SINE  IS NEGATIVE IN BOTH THE 3RD AND 4TH QUADRANT?

So theta (θ) must be in the 4th quadrant.

therefore sin(θ) = -1/3 is in the fourth quadrant. 

therefore arcsin of -1/3 = (θ).

So θ must equal -19.47 degrees approx.

the cos(-19.47°) = .9428

 

Answer 2

Hi Gayathree! When sin < 0, the y-part is pointing down ... Q3 or Q4 -- must be Q4 (+x, -1) for this problem ... x^2 = 3^2 - (-1)^2 = 8 ... x= +sqrt(8) where x >0 in Q4 ... cos ( )= sqrt(8) / 3 ... Best regards :)