Question

Why I have two answers for sine?!

SCa nd Simd V3 ろ Sin 8 y 8 2 fanod

Answer 1

"It is given that: - cosec (alpha) = -3, then tan alpha = ? if pi lesssthan alpha < 3 pi/2 (3rd quadrant) Because cosec (alpha) = -3 so sin (alpha) = -1/3 Implies sin (alpha) = -1/3 we know that in third quadrant sin function have -ve values, Here sin (alpha) = -1/3 where ""-"" sign is coming due to only for third quadrant Implies e know sin (pi + A) = -sin (A) (where 0 < A < pi/2) Let assume sin (alpha) = 1/3 = Height/Hypotense (To find out value in first quadrant) Base = squareroot (Hypo)^2 - (Height)^2 (Pythagorean) Base = squareroot (3)^2 - (1)^2 Base = squareroot 8 so tan alpha = Height/Base = 1/squareroot 8 Implies tan alpha = 1/squareroot 8 \r\n from here we can find out ""alpha"" which is ""key"" angle in first quadrant tan alpha = 1/squareroot 8 Implies alpha = tan^-1 (1/squareroot 8) But this angle belongs to alpha elementof "