Question

If sine of the quantity x plus y end quantity equals one half times sine of x plus radical 3 over 2 times cosine of x. What is the value of y?


A. pi over 2

B. pi over 3

C. pi over 4

D. pi over 6

Answer 1

The value of y from the given trig expression is pi/3 rad

Trigonometry identity

These identities are expressed in terms of sine, cosine and tangent

Given the expression

$sin(x+y)=\frac{1}{2}sinx+\frac{\sqrt{3}}{2} cosx$

Expand sin(x+y)

sin(x+y) = sinxcosy + cosxsiny

Compare both equations

cosy = 1/2

y = arccos(1/2)

y = 60 degrees

y = pi/3 rad

Hence the value of y from the given trig expression is pi/3 rad

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