Rewrite in terms of sin(x) and cos(x). sin(x+[7pi/4])

in terms of sin(x) and cos(x) s

The expression is given as:

Using sine rule, we have:

So, the expression becomes

7π/4 is corresponding to π/4.

So, we have:

Evaluate the sine and the cosine of the angle

Factor out √2 / 2

Hence, the equivalent of is

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using the addition formulae for sin

• sin(x + y ) = sinxcosy + cosxsiny

sin (x + (7π/4))

= sinx cos (7π/4) + cosxsin (7π/4)

[ the related acute angle for 7π/4 is π/4 ]

= sinxcos (π/4) + cosx (- sin (π/4 )

= sinx × √2 / 2 - cosx × √2 /2

= √2 / 2(sinx - cosx )

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