Find the range of f(x)=3 sinx +4 cosx -5
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ok, see take f(x) as y,
y+5=3sinx+4cosx
take coefficients of sinx and cosx , 3 & 4
square and add them and take whole root and take modulus.
|(3^2+4^2)^1/2| is ±5 ( this is the trick)
so -5<3sinx+4cosx<5
-5<y-5<5 as y-5 = 3sinx +4cosx
so add 5 and you will get
0<y<10 (answer)
hope it helps you.
y+5=3sinx+4cosx
take coefficients of sinx and cosx , 3 & 4
square and add them and take whole root and take modulus.
|(3^2+4^2)^1/2| is ±5 ( this is the trick)
so -5<3sinx+4cosx<5
-5<y-5<5 as y-5 = 3sinx +4cosx
so add 5 and you will get
0<y<10 (answer)
hope it helps you.
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0
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