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Example Express -8sinx° + 15cosx° in the form ksin(x +  )° ********* a = -8 & b = 15 kcos  ° = -8 and ksin  ° = 15 (kcos  °) 2 + (ksin  °) 2 = (-8)

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Presentation on theme: "Example Express -8sinx° + 15cosx° in the form ksin(x +  )° ********* a = -8 & b = 15 kcos  ° = -8 and ksin  ° = 15 (kcos  °) 2 + (ksin  °) 2 = (-8)"— Presentation transcript:

1 Example Express -8sinx° + 15cosx° in the form ksin(x +  )° ********* a = -8 & b = 15 kcos  ° = -8 and ksin  ° = 15 (kcos  °) 2 + (ksin  °) 2 = (-8) k 2 = k 2 = 289 k = 17 tan  ° = b / a = 15 / -8 kcos  °<0 Q2 or Q3 ksin  °>0 Q1 or Q2     in Q2 tan -1 ( 15 / 8 ) = 61.9° So -8sinx° + 15cosx° = 17sin(x )° Q2:  = 180 – 61.9 = 118.1°

2 Example (radians) Express  3 / 2 sin  - 1 / 2 cos  in the form ksin(  +  ) ********* a =  3 / 2 & b = - 1 / 2 kcos  =  3 / 2 and ksin  = - 1 / 2 (kcos  ) 2 + (ksin  ) 2 = (  3 / 2 ) 2 + (- 1 / 2 ) 2 k 2 = 3 / / 4 k 2 = 1 k = 1 tan  = b / a = ( -1 / 2 )  (  3 / 2 ) kcos  >0 Q1 or Q4 ksin  <0 Q3 or Q4    in Q4 tan -1 ( 1 /  3 )= 30° =  / 6 So  3 / 2 sin  - 1 / 2 cos  = sin(  + 11  / 6 ) Q4:  = 2  -  / 6 = 11  / 6 = -1 / 2 X ( 2 /  3 )= -1 /  3

3 VARIATIONS acosx° + bsinx° = kcos(x -  )° asinx° + bcosx° = ksin(x +  )° The usual formats are The variations kcos(x +  )° and ksin(x -  )° are easily obtained by considering reverse rotations from the X-axis. NB:-200° = +160° while +120° = -240° Sosin(x + 225)° = sin(x – 135)° and cos(  - 7  / 5 ) = cos(  + 3  / 5 )

4 Example Express 12sinx° - 5cosx° in the form ksin(x -  )° ********* a = 12 & b = -5 kcos  ° = 12 and ksin  ° = -5 (kcos  °) 2 + (ksin  °) 2 = (-5) 2 k 2 = k 2 = 169 k = 13 tan  ° = b / a = -5 / 12 kcos  °>0 Q1 or Q4 ksin  °<0 Q3 or Q4    in Q4 tan -1 ( 5 / 12 ) = 22.6° So 12sinx° - 5cosx° = 13sin(x )° = Q4:  = 360 – 22.6 = 337.4° 13sin(x – 22.6)°


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