Question

if cos theta has a negative value -29/21 then sin theta will be positive or negative???​

Answer 1

Answer:

Hope this helps.

(i) cos θ will never be -29/21 !!!  The values of cos θ are between -1 and 1 (inclusive).  Since -29/21 is less than -1, this is not a value that cos θ can take.

Nonetheless, in case it's helpful...

(ii) If cos θ is negative, then the angle is in the 2nd or 3rd quadrant, so sin θ can be either positive or negative.  If the angle is in the 2nd quadrant, then cos θ is negative and sin θ is positive.  If the angle is in the 3rd quadrant, then cos θ and sin θ are both negative.

 You might like to think of it as cos θ and sin θ are the x- and y-coordinates, respectively, of a point on the unit circle.  So in the 2nd quadrand (upper left), the x-coord (cos θ) is negative while the y-coord (sin θ) is positive.  In the 3rd quadrant (lower left), x- and y-coords (cos θ and sin θ) are both negative.