To solve for [tex]\(\cos 270^\circ\)[/tex], we start by understanding the position and properties of the given angle on the unit circle.
1. Identify the angle in standard position:
- [tex]\(270^\circ\)[/tex] is an angle measured from the positive x-axis, rotating clockwise. It lies on the negative y-axis.
2. Convert to radians for trigonometric calculations:
- To convert degrees to radians, use the formula: [tex]\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)[/tex].
- For [tex]\(270^\circ\)[/tex]:
[tex]\[
270^\circ \times \frac{\pi}{180} = \frac{270 \pi}{180} = \frac{3 \pi}{2} \text{ radians}
\][/tex]
3. Locate the angle on the unit circle:
- [tex]\(\frac{3 \pi}{2} \text{ radians}\)[/tex] points directly down the negative y-axis. This corresponds to the coordinates (0, -1) on the unit circle.
4. Apply the definition of cosine:
- The cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
- For [tex]\(\frac{3 \pi}{2} \text{ radians}\)[/tex], the coordinates are (0, -1). Thus, the x-coordinate is 0.
Therefore, [tex]\(\cos 270^\circ = 0\)[/tex].
Based on the options provided:
a. [tex]\(0\)[/tex] is the correct answer.
