Question

Question #c8ed2

Answer 1

`12sinvartheta+5cosvartheta=13sin(vartheta+0.394)`

Explanation:

`12sinvartheta+5cosvartheta=rsin(vartheta+varphi)`

`rsin(vartheta+varphi)=rsinvarthetacosvarphi+rcosvarthetasinvarphi`

Comparing coefficients, we find that `rsinvarphi=5` and `rcosvarphi=12`

`tanvarphi=(rsinvarphi)/(rcosvarphi)=5/12`

`varphi=arctan(5/12)=0.394^"rad"`

Since neither the unit of angular measurement nor accuracy were specified, I am using the standard unit of angular measurement, radians, and 3 sf. for accuracy.

`r=sqrt(sin^2varphi+cos^2varphi)=sqrt(5^2+12^2)=13`

`therefore12sinvartheta+5cosvartheta=13sin(vartheta+0.394)`

I shall leave ii) for another contributor