Find the value of the expression.Round your result to two decimal places. $\operatorname { arcsec } 3.14$
A)-1.25
B)1.25
C)1.89
D)3.14
E)-3.14

Question

Find the value of the expression.Round your result to two decimal places.   $\operatorname { arcsec } 3.14$  
A)-1.25 
B)1.25
C)1.89
D)3.14
E)-3.14

Quizplus · Accepted Answer

The arcsecant function, denoted as arcsec, is the inverse of the secant function. To find $\operatorname{arcsec}(3.14)$, we are essentially looking for an angle whose secant (the reciprocal of the cosine) is 3.14. The secant of an angle in a right triangle is the ratio of the length of the hypotenuse to the length of the adjacent side. Since secant is the reciprocal of cosine, we can use the relationship $\sec(\theta) = \frac{1}{\cos(\theta)}$. Therefore, we need to find $\theta$ such that $\frac{1}{\cos(\theta)} = 3.14$, which implies $\cos(\theta) = \frac{1}{3.14}$. Using a calculator to find the angle in radians that satisfies this equation and rounding to two decimal places gives us approximately 1.25 radians.

Find the Value of the Expression arcsec⁡3.14\operatorname { arcsec } 3.14arcsec3.14

Find the Value of the Expression $\operatorname { arcsec } 3.14$