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Find the maximum and minimum value of 8 cosA+15 sinA+15
- a)30, 8
- b)32, –2
- c)23, 8
- d)11√2+15, 15
Correct answer is option 'B'. Can you explain this answer?
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Find the maximum and minimum value of 8 cosA+15 sinA+15a)30, 8b)32, &n...
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Find the maximum and minimum value of 8 cosA+15 sinA+15a)30, 8b)32, &n...
To find the maximum and minimum value of the expression 8 cos(A) + 15 sin(A), we can use the fact that the maximum value of cos(A) + sin(A) is √2 and the minimum value is -√2.
First, let's find the maximum value:
The maximum value of 8 cos(A) + 15 sin(A) is equal to the maximum value of 8 cos(A) + 15 sin(A) when cos(A) and sin(A) both have their maximum values.
cos(A) has a maximum value of 1 when A = 0 degrees.
sin(A) has a maximum value of 1 when A = 90 degrees.
Therefore, the maximum value of 8 cos(A) + 15 sin(A) is 8(1) + 15(1) = 23.
Next, let's find the minimum value:
The minimum value of 8 cos(A) + 15 sin(A) is equal to the minimum value of 8 cos(A) + 15 sin(A) when cos(A) and sin(A) both have their minimum values.
cos(A) has a minimum value of -1 when A = 180 degrees.
sin(A) has a minimum value of -1 when A = 270 degrees.
Therefore, the minimum value of 8 cos(A) + 15 sin(A) is 8(-1) + 15(-1) = -23.
So, the maximum value is 23 and the minimum value is -23.
First, let's find the maximum value:
The maximum value of 8 cos(A) + 15 sin(A) is equal to the maximum value of 8 cos(A) + 15 sin(A) when cos(A) and sin(A) both have their maximum values.
cos(A) has a maximum value of 1 when A = 0 degrees.
sin(A) has a maximum value of 1 when A = 90 degrees.
Therefore, the maximum value of 8 cos(A) + 15 sin(A) is 8(1) + 15(1) = 23.
Next, let's find the minimum value:
The minimum value of 8 cos(A) + 15 sin(A) is equal to the minimum value of 8 cos(A) + 15 sin(A) when cos(A) and sin(A) both have their minimum values.
cos(A) has a minimum value of -1 when A = 180 degrees.
sin(A) has a minimum value of -1 when A = 270 degrees.
Therefore, the minimum value of 8 cos(A) + 15 sin(A) is 8(-1) + 15(-1) = -23.
So, the maximum value is 23 and the minimum value is -23.
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Find the maximum and minimum value of 8 cosA+15 sinA+15a)30, 8b)32, –2c)23, 8d)11√2+15, 15Correct answer is option 'B'. Can you explain this answer?
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