Use the sum and difference formula to determine the exact value of sin195

-0.259 or (√2 - √6) / 4

Step-by-step 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