Question

What is $\sec 180°$ degrees?

Answer 1

Finding the value of $\mathbf{sec}\mathbf{}\mathbf{180}\mathbf{°}$:

From the Trigonometric ratio, it is known that:

$$\begin{gathered} \mathbf{}\mathbf{sec}\mathbf{}\mathbf{x}\mathbf{=}\frac{\mathbf{1}}{\mathbf{cos}\mathbf{}\mathbf{x}} \\ \Rightarrow \sec 180°=\frac{1}{\cos 180°} \\ \Rightarrow \sec 180°=\frac{1}{-1}\mathbf{[}\mathbf{\because }\mathbf{cos}\mathbf{180}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{]} \\ \Rightarrow \sec 180°=-1 \end{gathered}$$

Hence, the value $\mathbf{sec}\mathbf{}\mathbf{180}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{1}$.