Given the trigonometric equation: find 3 positive solutions. explain how you found the solution : -)

The sine function is negative only in Quadrants III and IV.  The radius would be 2 and the opposite side would be -√3.  A similar triangle in the first Quadrant would have the central angle 60 degrees; note that sin 60 = opp/hyp √3 / 2.   Thus, one representation of the given sin y = -√3/2 would be (180 + 60) degrees, or +240 degrees.  Check for yourself that sin 240 degrees = -√3/2.

Another would be (360 - 60) degrees, or 300 degrees.  Note that sin 300 degrees = -√3/2.  

A third would be (300 + 360) degrees, or 660 degrees.  Verify that sin 660 = -√3 / 2.

Three positive angles whose sines are all -√3/2 are {240, 300, 660}.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.