Question

Find the exact value of sin –255°.

Answer 1

sin(-255°) = √2 + √6/4

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