cos 90 degrees
Understand the Problem
The question is asking for the value of the cosine function at an angle of 90 degrees. This is a trigonometric question, specifically dealing with the use of the unit circle.
Answer
0
Answer for screen readers
The final answer is 0
Steps to Solve
- Understanding the unit circle
The unit circle is a circle with a radius of 1 centered at the origin (0,0) of a coordinate plane. The angle in trigonometry is measured from the positive x-axis in a counter-clockwise direction.
- Identify the point on the unit circle at 90 degrees
At 90 degrees, the point on the unit circle is at the top of the circle. The coordinates of this point are $(0,1)$.
- Determine the cosine value from the coordinates
The cosine of an angle in the unit circle is the x-coordinate of the corresponding point. For 90 degrees, the x-coordinate is 0.
Thus, the value of $\cos 90^\circ$ is 0.
The final answer is 0
More Information
In trigonometry, the value of $\cos 90^\circ = 0$. This is because at 90 degrees, the point on the unit circle is (0,1) and the x-coordinate is taken as the cosine value.
Tips
A common mistake is confusing the coordinates. Remember that cosine is the x-coordinate and sine is the y-coordinate on the unit circle.
