what is the maximum value of 3cos theta - 4sin theta + 10
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The maximum value is 15
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Hey !!!
let y = 3cos¢ - 4sin¢ + 10
°•° √3² + 4² = √9 + 16 = √25 = 5
multiply and divide by 5
y = 5( 3/5cos¢ - 4/5sin¢ ) + 10
let that 3/5 = cos@ and 4/5 = sin@
y = 5 ( cos@ cos¢ - sin@ sin¢ ) + 10
y = 5 { cos ( @ - ¢ ) } + 10
but , maximum value of cos( @ + ¢ ) is 1
hence,
y = 5× 1 + 10
y = 15
15 is the maximum value of 3cos¢ - 4sin¢ + 10
____________________________
Hope it helps you !!!
@Rajukumar111
let y = 3cos¢ - 4sin¢ + 10
°•° √3² + 4² = √9 + 16 = √25 = 5
multiply and divide by 5
y = 5( 3/5cos¢ - 4/5sin¢ ) + 10
let that 3/5 = cos@ and 4/5 = sin@
y = 5 ( cos@ cos¢ - sin@ sin¢ ) + 10
y = 5 { cos ( @ - ¢ ) } + 10
but , maximum value of cos( @ + ¢ ) is 1
hence,
y = 5× 1 + 10
y = 15
15 is the maximum value of 3cos¢ - 4sin¢ + 10
____________________________
Hope it helps you !!!
@Rajukumar111
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