What is the Value of Sec 0 Degrees ?

Solution :

The value of Sec 0 degrees is equal to 1.

Proof :

\(\angle\) A is made smaller and smaller in the right \(\Delta\) ABC till it becomes zero. As \(\angle\) A gets smaller and smaller the length of the side BC decreases. The point C gets closer to the point B and finally when \(\angle\) A becomes very close to 0 degrees, AC becomes almost the same as AB, and BC gets very close to 0.

0 degrees

By using trigonometric formula,

Sec A = \(hypotenuse\over base\) = \(h\over b\)

AC is nearly becoming the same as AB.

Sec A = \(AC\over AB\) = \(AB\over AB\) = 1

Hence,  \(sec 0^{\circ}\) = 1

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