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 and Rsin⁡(x+a)=6, I don't know how to proceed.

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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 and Rsin⁡(x+a)=6, I don&#039;t know how to proceed.

ramirezhereva · Accepted Answer

Starting from R=66,a=arcsin⁡765 we have  65sin⁡(x+a)=6   ⇒x=arcsin⁡665−a=arcisn665−arcsin⁡765  Using  arcsin⁡u−arcsin⁡v=arcsin⁡(u1−v2−v1−u2)   x=arcsin⁡(665⋅465−765⋅65−6265)  x=arcsin⁡(24−72965)

Vasquez · Accepted Answer

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

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...

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