write the function in terms of the cofunction of a complementary angle.\n\\( \\csc \\frac { 5 \\pi } { 24 }…

write the function in terms of the cofunction of a complementary angle.\n\\( \\csc \\frac { 5 \\pi } { 24 } \\)\n\\( \\csc \\frac { 5 \\pi } { 24 } = \\square \\) (simplify your answer.)

write the function in terms of the cofunction of a complementary angle.\n\\( \\csc \\frac { 5 \\pi } { 24 } \\)\n\\( \\csc \\frac { 5 \\pi } { 24 } = \\square \\) (simplify your answer.)

Answer

Explanation:

Step1: Recall the co - function identity

The co - function identity for cosecant is (\csc\theta=\sec\left(\frac{\pi}{2}-\theta\right)).

Step2: Substitute (\theta = \frac{5\pi}{24}) into the identity

We have (\frac{\pi}{2}-\frac{5\pi}{24}=\frac{12\pi}{24}-\frac{5\pi}{24}). [ \begin{align*} \frac{12\pi}{24}-\frac{5\pi}{24}&=\frac{12\pi - 5\pi}{24}\ &=\frac{7\pi}{24} \end{align*} ] Since (\csc\theta=\sec\left(\frac{\pi}{2}-\theta\right)), when (\theta=\frac{5\pi}{24}), (\csc\frac{5\pi}{24}=\sec\left(\frac{\pi}{2}-\frac{5\pi}{24}\right))

Answer:

(\sec\frac{7\pi}{24})