Range of 3 sin theta+4 cos theta+2=?

Consider the expression.     3sinθ+4cosθ+2Note that the range of cosine function cosθ is -1,1Also,  the range of sine function sinθ is -1,1This implies that,      -1sinθ1      and   -1cosθ1This further implies that,       -33sinθ3      and   -44cosθ4So the minimum value of the given expression will be       -3-4+2=-5and the maximum value of the given expression will be          3+4+2=9So the range of  3sinθ+4cosθ+2 is -5,9

  • -3
-5 to 9
  • -1
[-3,7]
  • -1
let theta = x (for typing comforts)

Meethi,   there is a formula .... for f(x) = a sinx + b cosx + c .....  range of f(x) is from "-1 * [root(a^2 + b^2)] + c" to ​"root(a^2 + b^2) + c" (closed intervals)

so using that ..... ans is [-3,7] 

Hope it helps u!!! .... if it does .... do thumbs up
  • 1
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