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

1.	Find the greatest and least values of 4sin theta +3cos beta +7
Answer» 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.

Answer»

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.

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