Use an Addition or Subtraction Formula to find the exact value of the expression: sin 255°

Solution:

Given function sin255°

We can re-write the function as sin(75 + 180) for easier calculation

sin 255° = sin (75° + 180°) = -sin 75°.

Let’s find sin 75° by using the trignometric identity:

sin (a + b) = sin a.cos b + sin b.cos a

Now, sin 75° = sin (30° + 45°) 

sin75°= sin 30°.cos 45° + sin 45°.cos 30°

We know that sin30° = 1/2 , sin45° = 1/√2 , cos30° = √3/2 and cos45° = 1/√2

Substitute these values,

sin75° = (1/2)(1/√2) + (1/√2)(√3/2)

sin75°= (1/√2)(1/2 + √3/2) 

= √2 + √6 /4 [by multiplying and dividing by √2 ]

Finally, sin255° = -sin75°

= -{√2 + √6} /4

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Use an Addition or Subtraction Formula to find the exact value of the expression: sin 255°

Summary:

By using an Addition or Subtraction Formula to find the exact value of the expression: we got sin 255° = -{√2 + √6} /4