Question

Acute angle W has sin W = 1/2 and sec W = 2/square root 3. Which are values of csc W and cos W?

Answer 1

We are given that \( \sin W = \frac{1}{2} \) and \( \sec W = \frac{2}{\sqrt{3}} \).

First, let's find \( \cos W \) using the relationship between sine and secant. Remember that:

\[
\sec W = \frac{1}{\cos W}
\]

From \( \sec W = \frac{2}{\sqrt{3}} \), we find \( \cos W \):

\[
\cos W = \frac{1}{\sec W} = \frac{\sqrt{3}}{2}
\]

Next, we'll find \( \csc W \) using the relationship between sine and cosecant:

\[
\csc W = \frac{1}{\sin W}
\]

Substituting the value of \( \sin W \):

\[
\csc W = \frac{1}{\frac{1}{2}} = 2
\]

To summarize, the values of \( \csc W \) and \( \cos W \) are:

\[
\csc W = 2
\]
\[
\cos W = \frac{\sqrt{3}}{2}
\]