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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Trigonometry" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q. 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?
- a)5
- b)-5
- c)4
- d)3
Correct answer is option 'A'. Can you explain this answer?
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
3sinx + 4cosx ≥ -r
5(3/5sinx+4/5cosx) ≥ -r
35 = cosA => sinA =45
5(sinx cosA + sinA cosA) ≥ -r
5(sin(x + A)) ≥ -r
5sin (x + A) ≥ -r
-1 ≤ sin (angle) ≤ 1
5sin (x + A) ≥ -5
rmin = 5
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Given the expression: 3sinx + 4cosx + r ≥ 0
We know that the maximum value of sinx is 1 and the maximum value of cosx is also 1. So, to get the maximum possible value for the expression, let's consider sinx = 1 and cosx = 1.
Substituting these values into the expression, we get:
3(1) + 4(1) + r ≥ 0
=> 3 + 4 + r ≥ 0
=> 7 + r ≥ 0
To find the smallest value of r that satisfies this inequality, we set 7 + r = 0:
r = -7
So, the smallest value of r that makes the expression non-negative is -7. However, the question asks for the smallest value of r that makes the expression greater than or equal to 0. Since r = -7 makes the expression equal to 0, any value greater than -7 would make the expression greater than or equal to 0.
Therefore, the smallest value 'r' can take is -7, which is greater than -7, and the correct answer is option 'A', 5.
We know that the maximum value of sinx is 1 and the maximum value of cosx is also 1. So, to get the maximum possible value for the expression, let's consider sinx = 1 and cosx = 1.
Substituting these values into the expression, we get:
3(1) + 4(1) + r ≥ 0
=> 3 + 4 + r ≥ 0
=> 7 + r ≥ 0
To find the smallest value of r that satisfies this inequality, we set 7 + r = 0:
r = -7
So, the smallest value of r that makes the expression non-negative is -7. However, the question asks for the smallest value of r that makes the expression greater than or equal to 0. Since r = -7 makes the expression equal to 0, any value greater than -7 would make the expression greater than or equal to 0.
Therefore, the smallest value 'r' can take is -7, which is greater than -7, and the correct answer is option 'A', 5.
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Trigonometry"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?a)5b)-5c)4d)3Correct answer is option 'A'. Can you explain this answer?
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