Question
Sun April 03, 2011 By: Theodosia Lourdes
 

What is the maximum and minimum value of sin ? and cos ? ? Explain how.

Expert Reply
Mon April 04, 2011
Dear Student,

Properties Of The Sine Graph

 

The sine function forms a wave that starts from the origin

  • sin θ = 0 when θ = 0 ˚ , 180˚ , 360˚ .
  • Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.
  • As the point θ moves round the unit circle in either the clockwise or anticlockwise direction, the sine curve above repeats itself for every interval of 360˚. The interval over which the sine wave repeats itself is called the period.

Properties Of The Cosine Graph

 
  • The cosine function forms a wave that starts from the point (0,1)
  • cos θ = 0 when θ = 90 ˚ , 270˚ .
  • Maximum value of cos θ is 1 when θ = 0 ˚, 360˚. Minimum value of cos θ is –1 when θ = 180 ˚. So, the range of values of cos θ is – 1 ≤ cos θ ≤ 1.
  • As the point P moves round the unit circle in either the clockwise or anticlockwise direction, the cosine curve above repeats itself for every interval of 360˚. Its period is 360˚.
Hope this clears your doubts.
Regards
Team Topperlearning
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