Find the exact value of sin - 255°.

sin (-255°) = √2 + √6/4

Step-by-step explanation:

We need to find sin - 255°

We know that sin (-a) = - sin (a)

so, sin (-255°) = - sin 255°

We know that 180° + 75° = 255°

Now we can write sin (255°) = sin (180° + 75°)

We can use the identity:

sin (x+y) = sin (x) cos (y) + cos (x) sin (y)

x = 180°, y = 75°

Solving,

sin (x+y) = sin (x) cos (y) + cos (x) sin (y)

sin (180° + 75°) = sin (180°) cos (75°) + cos (180°) sin (75°)

sin (180°) = 0

cos (75°) = √6 - √2/4

cos (180°) = - 1

sin (75°) = √2 + √6/4

Putting values,

sin (180° + 75°) = 0 (√6 - √2/4) + (-1) (√2 + √6/4)

sin (180° + 75°) = - (√2 + √6/4)

We know that sin (-255°) = - sin (255°)

Putting value of sin (255°)

sin (-255°) = - ( - (√2 + √6/4))

sin (-255°) = √2 + √6/4