Question

Find the range of f(x)=3 sinx +4 cosx -5

Answer 1

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.

Answer 2

Answer:

find the cube root of 27 25