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F.4 A.Maths
If the equation 4cos(x + 45°) + k sin (x + 45°) = p sin x holds for all values of x, find the values of the constants k and p.
最佳解答:
If the equation 4cos(x+45°)+ksin(x+45°)=psinx holds for all values of x, find the values of the constants k and p. As 4cos(x+45°) + ksin(x+45°) = psinx ... (#) holds for all real values of x Put x = 0° into (#) 4cos(0°+45°) + ksin(0°+45°) = psin(0°) 4cos45° + ksin45° = p(0) 4(√2/2) + k(√2/2) = 0 4 + k = 0 k = -4 Put x = -45° into (#) 4cos(-45°+45°) + ksin(-45°+45°) = psin(-45°) 4cos0° + ksin0° = p(-sin45°) 4(1) + k(0) = -p(√2/2) p = -8/√2 p = -4√2
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F.4 A.Maths
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發問:If the equation 4cos(x + 45°) + k sin (x + 45°) = p sin x holds for all values of x, find the values of the constants k and p.
最佳解答:
If the equation 4cos(x+45°)+ksin(x+45°)=psinx holds for all values of x, find the values of the constants k and p. As 4cos(x+45°) + ksin(x+45°) = psinx ... (#) holds for all real values of x Put x = 0° into (#) 4cos(0°+45°) + ksin(0°+45°) = psin(0°) 4cos45° + ksin45° = p(0) 4(√2/2) + k(√2/2) = 0 4 + k = 0 k = -4 Put x = -45° into (#) 4cos(-45°+45°) + ksin(-45°+45°) = psin(-45°) 4cos0° + ksin0° = p(-sin45°) 4(1) + k(0) = -p(√2/2) p = -8/√2 p = -4√2
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