Question

Most calculators do not have a key to evaluate sec−1 (2). Explain how this can be done using the cosine function or the inverse cosine function.

Answer 1

Consider the expression sec-1(2)

To solve the expression use cosine function as follows,

 

Let x = sec-1(2)

 

Take Secant on each side to solve further with use of cosine function,

    secx = sec{sec-1(2)}

    secx = 2

1/cosx = 2

      1/2 = cosx

 

Solve further,

  1/2 = cosx

cosx = cos(π/3)

      x = π/3

 

Or,

1/2 = cos x

   x = cos-1(1/2)

   x = π/3

 

It can be seen from the above equations that with the use of cosine and inverse cosine functions the expression sec-1(2) can be solved without use of calculator.

It can be seen from the above equations that with the use of cosine and inverse cosine functions the expression sec-1(2) can be solved without use of calculator.