Question

Which of the following best represents the value of arcsec 1.6 in degrees, using the standard restricted domain?

39°
51°
78°
128°

Answer 1

`51\°`

Explanation:

we know that

`sec(x)=(1)/(cos(x))`

In this problem we have

`sec(x)=1.6`

so

`x=arcsec(1.6)` -----> equation A

`1.6=(1)/(cos(x))`

`cos(x)=(1)/(1.6)`

`x=arccos((1)/(1.6))` ---> equation B

equate equation A and equation B

`arcsec(1.6)=arccos((1)/(1.6))`

`arcsec(1.6)=51\°`