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 ÃŽÂ¸ = 0 when ÃŽÂ¸ = 0 Ã‹Âš , 180Ã‹Âš , 360Ã‹Âš .
• Maximum value of sin ÃŽÂ¸ is 1 when ÃŽÂ¸ = 90 Ã‹Âš. Minimum value of sin ÃŽÂ¸ is Ã¢Â€Â“1 when ÃŽÂ¸ = 270 Ã‹Âš. So, the range of values of sin ÃŽÂ¸ is Ã¢Â€Â“1 Ã¢Â‰Â¤ sin ÃŽÂ¸ Ã¢Â‰Â¤ 1.
• As the point ÃŽÂ¸ moves round the unit circle in either the clockwise or anticlockwise direction, the sine curve above repeats itself for every interval of 360Ã‹Âš. 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 ÃŽÂ¸ = 0 when ÃŽÂ¸ = 90 Ã‹Âš , 270Ã‹Âš .
• Maximum value of cos ÃŽÂ¸ is 1 when ÃŽÂ¸ = 0 Ã‹Âš, 360Ã‹Âš. Minimum value of cos ÃŽÂ¸ is Ã¢Â€Â“1 when ÃŽÂ¸ = 180 Ã‹Âš. So, the range of values of cos ÃŽÂ¸ is Ã¢Â€Â“ 1 Ã¢Â‰Â¤ cos ÃŽÂ¸ Ã¢Â‰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 360Ã‹Âš. Its period is 360Ã‹Âš.