which equation should be used to graph y = sec⁻¹(x) on a calculator?\no y = 1/sec(x)\no y = 1/cos⁻¹(x)\no y…
which equation should be used to graph y = sec⁻¹(x) on a calculator?\no y = 1/sec(x)\no y = 1/cos⁻¹(x)\no y = sec(1/x)\no y = cos⁻¹(1/x)
Answer
Explanation:
Step1: Recall secant - cosine relationship
We know that $\sec(x)=\frac{1}{\cos(x)}$. Let $y = \sec^{-1}(x)$, then $\sec(y)=x$, which means $\frac{1}{\cos(y)}=x$, or $\cos(y)=\frac{1}{x}$.
Step2: Solve for y
Solving $\cos(y)=\frac{1}{x}$ for $y$ gives $y=\cos^{-1}(\frac{1}{x})$.
Answer:
$y=\cos^{-1}(\frac{1}{x})$ (the fourth option)