Question

c) Without using calculator find the value of sin ( 3660)

Answer 1

Answer:

hope answer was helpful

Answer 2

Given:

A trigonometric function Sin( 3660° ).

To Find:

The value of the above function.

Solution:

The given problem can be solved using the concepts of trigonometry.

1. The given trigonometric term is Sin( 3660°).  

2. According to the properties of trigonometry,

=> Sin ( 360 + x ) = Sinx.

3. Using the property mentioned above we can find the value of Sin( 3660°),

=> Sin(3660°) = Sin(360 + 3300) = Sin(3300°),

=> Sin(3300) = Sin(360+2940) = Sin(2940°),

=> Sin(2940) = Sin(360+2580) = Sin(2580°),

=> Sin(2580) = Sin(360+2220) = Sin(2220°),

=> Sin(2200) = Sin(360 + 1840) = Sin(1860°),

=> Sin(1840) = Sin(360 + 1480) = Sin(1500°),

=> Sin(1480) = Sin(360 + 1120) = Sin(1140°),

=> Sin(1120) = Sin(360 + 780) = Sin(780°),

=> Sin(760) = Sin(360 + 420) = Sin(420°),

=> Sin(420) = Sin(360 + 60) = Sin(60°).

4. The value of Sin(60°) is √(3)/2.

Hence, the value of Sin(3660°) is √(3)/2.