Question

Without using calculator find the value of sec(3660°)

Answer 1

Given:  

A trigonometric function sec(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 sec(3660°).

2. According to the properties of trigonometry,  

=> Sec( 360 + x ) = Secx.  

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

=> sec(3660°) = Sec(360 + 3300) = Sec(3300°),  

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

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

=> Sec(2580) = Sec(360 + 2200) = Sec(2220°),  

=> Sec(2220) = Sec(360 + 1860) = Sec(1860°),  

=> Sec(1860) = Sec(360 + 1500) = Sec(1500°),  

=> Sec(1500) = Sec(360 + 1140) = Sec(1140°),  

=> Sec(1140) = Sec(360 + 780) = Sec(780°),  

=> Sec(780) = Sec(360 + 420) = Sec(420°),  

=> Sec(420) = Sec(360 + 60) = Sec(60°),

4. The value of Sec(60°) is,

=> Sec(60°) = 1/(cos(60°)) = 2.

Hence, the value of Sec(3660°) is 2.