Answer:
-0.259 or (√2 - √6) / 4
Explanation:
Sin (195) using sum and difference formula.
Let's break the figure for convenience.
It becomes sin ( 135 + 60)
Invoking the sin formula we have
sin (A + B) = sin (A) cos (B) + cos (A) sin(B)
Where A = 135, B = 60
Therefore it becomes
sin(135) cos(60) + cos(135) sin (60)
From reference angle relationship we have:
(sin (45))cos (60) + cos (135) sin (60)
From trigonometric ratios, sin (45) = √2/2
Therefore, the equation becomes,
(√2/2) cos(60) + cos (135)sin (60)
(√2/2) (0.5) + cos (135) sin (60)
= (√2/2) (1/2) + ( - √2/2) ( √3/2)
Simplifying the equation
√2/4 + ( -√2/2) ( √3/2)
= √2/4 - √6/4
= (√2 - √6) / 4
OR
=( 1.414 - 2.449 ) / 4
= -1.035/4
= -0.25875