4sin⁡(x)+7cos⁡(x)=6where 0≤x≤360∘I put the equation into the form asin⁡(x)+bcos⁡(x)=Rsin⁡(x+a), but after determining that Rcos⁡(a)=4, Rsin⁡(a)=7...

aspifsGak5u

aspifsGak5u

Answered

2022-01-03

4sin(x)+7cos(x)=6
where 0x360
I put the equation into the form asin(x)+bcos(x)=Rsin(x+a), but after determining that Rcos(a)=4, Rsin(a)=7 and Rsin(x+a)=6, I don't know how to proceed.

Answer & Explanation

ramirezhereva

ramirezhereva

Expert

2022-01-04Added 28 answers

Starting from R=66,a=arcsin765 we have
65sin(x+a)=6
x=arcsin665a=arcisn665arcsin765
Using
arcsinuarcsinv=arcsin(u1v2v1u2)
x=arcsin(665465765656265)
x=arcsin(2472965)
Vasquez

Vasquez

Expert

2022-01-08Added 457 answers

HINT:
NSK
The R is related to
so that sina=765,cosa=465
which is more convenient. Divide both sides by 65
sin(x+a)=665
where
tanα=74

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