Differentiation

Question

sin(x)=7root 2/10.

hence show that sin(x+pi/4) = 0.8 

Answer 1

Since sinx > 0, x lies in the first or second quadrant.

 

Assuming that x lies in the first quadrant, cosx = √(1 - sin²x) = √(1 - (49/50))

        

                                                                                          = 1/(5√2) = √2/10

sin(x + π/4) = sinx cos(π/4) + cosx sin(π/4)

 

                   = (√2/2)(sinx + cosx))

 

                   = (√2/2)[7√2/10 + √2/10]

 

                   = (√2/2)(4√2/5) = 8/10 = 0.8.