Question

8 cos theta + 15 sin theta =?

options have
a) 18
b) 19
c) 17
d) 20

pls tell me the correct answer , if anyone know.....

Answer 1

Answer:

17

Step-by-step explanation:

8 cos theta + 15 sin theta =?

options have  

a) 18

b) 19

c) 17

d) 20

We need to find Maximum value of

8Cosθ + 15Sinθ  

Differentiating wrt to θ

d(8Cosθ)/dθ + d(15Sinθ)/dθ = 0

=> -8Sinθ + 15Cosθ = 0

=> 8Sinθ = 15Cosθ

=> Sinθ/Cosθ = 15/8

=> Tanθ = 15/8

Tanθ = 15/8 will give maximum value for 8Cosθ + 15Sinθ

Tanθ = P/B

Hypotenuse = √(15² + 8²) = 17

Sinθ = P/H = 15/17

Cosθ = B/H = 8/17

putting values of Sinθ & Cosθ

8Cosθ + 15Sinθ  

= 8(8/17)  + 15(15/17)

= (64 + 225)/17

= 289/17

= 17

option C is the right answer