Question

Find the maximum value of 5cosA + 12sinA + 12

Answer 1

Answer:

5cos(A)+12sin(A)+12=13(513cos(A)+1213sin(A))+12 .

As

(513)2+(1213)2=1 ,

there exists a number  φ  ( 0≤φ<2π ), so that

cos(φ)=513sin(φ)=1213 .

If fact  0<φ<π2 .

Then we can write the original expression as

13(cosAcosφ+sinAsinφ)+12=13cos(A−φ)+12 .

The maximum of this function occurs when  A=φ  and its value is  13+12=25 .

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Answer 2

Answer:

5cos(A)+12sin(A)+12=13(513cos(A)+1213sin(A))+12

Step-by-step explanation:

As

(513)2+(1213)2=1 ,

there exists a number φ ( 0≤φ<2π ), so that

cos(φ)=513sin(φ)=1213 .

If fact 0<φ<π2 .

Then we can write the original expression as

13(cosAcosφ+sinAsinφ)+12=13cos(A−φ)+12