Question

How do you simplify `Sin (pi/6 + x)`?

Answer 1

`1/2cosx+sqrt3/2sinx`

Explanation:

Using the appropriate`color(blue)" Addition formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)sinAcosB±cosAsinB)color(white)(a/a)|)))`

then `sin(pi/6+x)=sin(pi/6)cosx+cos(pi/6)sinx`

Using the`color(blue)" exact value triangle ""for this angle"`

Then `sin(pi/6)=1/2" and " cos(pi/6)=sqrt3/2`

`rArrsin(pi/6+x)=1/2cosx+sqrt3/2sinx`