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Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done?
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Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d...
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Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d...
To find the value of A in the equation 3sin(theta) + 4cos(theta) = A*sin(theta + phi), where phi is a constant angle, we can use the properties of trigonometric functions and algebraic manipulation.
1. Start by rearranging the equation:
3sin(theta) + 4cos(theta) = A*sin(theta + phi)
2. Use the trigonometric identity sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B) to rewrite the right side of the equation:
A*sin(theta + phi) = A*sin(theta)*cos(phi) + A*cos(theta)*sin(phi)
3. Compare the coefficients of sin(theta) and cos(theta) on both sides of the equation:
3 = A*cos(phi)
4 = A*sin(phi)
4. Square both equations to eliminate the trigonometric functions:
3^2 = (A*cos(phi))^2
4^2 = (A*sin(phi))^2
Simplify:
9 = A^2*cos^2(phi)
16 = A^2*sin^2(phi)
5. Use the trigonometric identity sin^2(phi) + cos^2(phi) = 1 to eliminate the trigonometric functions:
9 + 16 = A^2*(sin^2(phi) + cos^2(phi))
25 = A^2
6. Take the square root of both sides:
sqrt(25) = sqrt(A^2)
5 = A
Therefore, the value of A is 5. Thus, the correct answer is option c) 5.
1. Start by rearranging the equation:
3sin(theta) + 4cos(theta) = A*sin(theta + phi)
2. Use the trigonometric identity sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B) to rewrite the right side of the equation:
A*sin(theta + phi) = A*sin(theta)*cos(phi) + A*cos(theta)*sin(phi)
3. Compare the coefficients of sin(theta) and cos(theta) on both sides of the equation:
3 = A*cos(phi)
4 = A*sin(phi)
4. Square both equations to eliminate the trigonometric functions:
3^2 = (A*cos(phi))^2
4^2 = (A*sin(phi))^2
Simplify:
9 = A^2*cos^2(phi)
16 = A^2*sin^2(phi)
5. Use the trigonometric identity sin^2(phi) + cos^2(phi) = 1 to eliminate the trigonometric functions:
9 + 16 = A^2*(sin^2(phi) + cos^2(phi))
25 = A^2
6. Take the square root of both sides:
sqrt(25) = sqrt(A^2)
5 = A
Therefore, the value of A is 5. Thus, the correct answer is option c) 5.
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Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done?
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Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done?.
Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find A if 3sin theta +4cos theta =A sin (theta +fie ) a) 7 b) 1 c) 5 d)25 the correct answer is c .Can anyone explain how this is done?.
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