Question

find a cofunction with the same value as the given expression.
csc 11°

select the correct choice below and fill in the answer box to complete your choice.
(simplify your answer. type any angle measures in degrees. do not include the degree symbol in your answer.)
a. csc 11° = cot □°
b. csc 11° = cos □°
c. csc 11° = tan □°
d. csc 11° = sin □°
e. csc 11° = sec □°

Explanation:

Step1: Recall cofunction identities

We know that the cofunction identity for cosecant and secant is \(\csc\theta=\sec(90^{\circ}-\theta)\).

Step2: Apply the identity to \(\csc11^{\circ}\)

Substitute \(\theta = 11^{\circ}\) into the identity \(\csc\theta=\sec(90 - \theta)\). So we have \(\csc11^{\circ}=\sec(90 - 11)^{\circ}=\sec79^{\circ}\). Also, we check the options, option E is in terms of secant. So we use this identity to find the angle.

Answer:

E. \(\csc 11^{\circ}=\sec 79\)