Question

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

Answer 1

To find \( \csc W \) and \( \cos W \) given that \( \sin W = \frac{1}{2} \) and \( \sec W = \frac{2}{\sqrt{3}} \), we can use the relationships between the trigonometric functions.

1. **Calculating \( \csc W \)**:
The cosecant function is the reciprocal of the sine function:
\[
\csc W = \frac{1}{\sin W}
\]
Substituting the given value of \( \sin W \):
\[
\csc W = \frac{1}{\frac{1}{2}} = 2
\]

2. **Calculating \( \cos W \)**:
The secant function is the reciprocal of the cosine function:
\[
\sec W = \frac{1}{\cos W}
\]
Substituting the given value of \( \sec W \):
\[
\frac{1}{\cos W} = \frac{2}{\sqrt{3}}
\]
Taking the reciprocal gives:
\[
\cos W = \frac{\sqrt{3}}{2}
\]

Thus, the values of \( \csc W \) and \( \cos W \) are:
\[
\csc W = 2
\]
\[
\cos W = \frac{\sqrt{3}}{2}
\]