Question

find the greatest and least values of 4sin theta +3cos beta +7

Answer 1

Answer ⇒ Maximum Value = 14.

Minimum value = 0.

Step-by-step explanation ⇒

Now, The value of the Expression will be maximum and minimum when the sine and cosine will be maximum and minimum respectively.

The maximum value of sine and cosine function is  +1.

Thus, Maximum Sinθ = Cosβ = 1.

For Maximum, the Expression,

4Sinθ + 3Cosβ + 7 = 4 + 3 + 7

= 14.

Now, The Minimum value of sine and cosine function is -1.

∴ Minimum value of the Expression is,

4Sinθ + 3Cosβ + 7 = 4(-1) + 3(-1) + 7

= -7 + 7

= 0

Maximum Value = 14.

Minimum value = 0.

Hope it helps.