Sin100*cos300

To calculate \( \sin(100^\circ) \cos(300^\circ) \), we can first simplify \( \cos(300^\circ) \). The angle \( 300^\circ \) is in the fourth quadrant, and can be expressed as: \[ 300^\circ = 360^\circ - 60^\circ \] Thus, we can use the cosine identity for angles: \[ \cos(300^\circ) = \cos(360^\circ - 60^\circ) = \cos(60^\circ) = \frac{1}{2} \] Now, we have: \[ \sin(100^\circ) \cos(300^\circ) = \sin(100^\circ) \cdot \frac{1}{2} \] Next, we need to find \( \sin(100^\circ) \). The sine function is positive in the first and second quadrants. Using a calculator or sine tables, we find that: \[ \sin(100^\circ) \approx 0.9848 \] Therefore: \[ \sin(100^\circ) \cdot \frac{1}{2} \approx 0.9848 \cdot \frac{1}{2} = 0.4924 \] Thus, the value of \( \sin(100^\circ) \cos(300^\circ) \) is approximately \( 0.4924 \).