`sec(arctan(-3/5))` Find the exact value of the expression. (Hint: Sketch a right triangle.)

balajia | Student

`tan^-1(-3/5) = -tan^-1(3/5)`

Taking 3 as opposite side and 5 as adjacent side , then the hypotenuse will be `sqrt(5^2+3^2)=sqrt(34).`

`tan^-1(3/5)=sec^-1(sqrt(34)/5)`

`sec(tan^-1(-3/5)) = sec(-tan^-1(3/5))`

`=sec(tan^-1(3/5))=sec(sec^-1(sqrt(34)/5))=sqrt(34)/5`

`=1.166.`