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Question
Sun April 03, 2011

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

Mon April 04, 2011
Dear Student,

Properties Of The Sine Graph

The sine function forms a wave that starts from the origin

• sin Î¸ = 0 when Î¸ = 0 Ë , 180Ë , 360Ë .
• Maximum value of sin Î¸ is 1 when Î¸ = 90 Ë. Minimum value of sin Î¸ is â1 when Î¸ = 270 Ë. So, the range of values of sin Î¸ is â1 â¤ sin Î¸ â¤ 1.
• As the point Î¸ moves round the unit circle in either the clockwise or anticlockwise direction, the sine curve above repeats itself for every interval of 360Ë. 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 Î¸ = 0 when Î¸ = 90 Ë , 270Ë .
• Maximum value of cos Î¸ is 1 when Î¸ = 0 Ë, 360Ë. Minimum value of cos Î¸ is â1 when Î¸ = 180 Ë. So, the range of values of cos Î¸ is â 1 â¤ cos Î¸ â¤ 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 360Ë. Its period is 360Ë.