How do I find tan(-pi/4) from the unit circle?
Thanks.
Go 45 degrees clockwise or reverse of the circle, it should be at 315 degrees.
To find the value of tan(-π/4) from the unit circle, you need to follow these steps:
1. Start by understanding the angles and coordinates on the unit circle. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. The circumference of the unit circle is divided into 360 degrees or 2π radians.
2. Since the given angle is -π/4, which is equivalent to -45 degrees, we need to find the point on the unit circle that corresponds to that angle.
3. In the unit circle, angles are measured counterclockwise from the positive x-axis. So, to find -45 degrees, you need to go 45 degrees clockwise from the positive x-axis or reverse direction. This will bring you to the point at 315 degrees (or -45 degrees).
4. The point at 315 degrees corresponds to the coordinate (-√2/2, -√2/2) on the unit circle. This can be determined by using the values of cos(315 degrees) = -√2/2 and sin(315 degrees) = -√2/2.
5. Finally, to find the tangent of the angle -π/4 or -45 degrees, you use the formula tan(theta) = sin(theta) / cos(theta). So, tan(-π/4) = sin(-π/4) / cos(-π/4) = (-√2/2) / (-√2/2) = 1.
Therefore, the value of tan(-π/4) from the unit circle is 1.