How do I use the unit circle to evaluate tan(-3pi/4)
draw the circle and the line at the given angle. The intersection will give you a point (x,y).
in this case, the line is at an angle of 45 degrees, in QIII, where y=x.
tan (-3pi/4) = (-1√2)/(-1/√2) = 1
To use the unit circle to evaluate tan(-3π/4), first let's understand what the unit circle is and how it can help us evaluate trigonometric functions like tangent.
The unit circle is a circle with a radius of 1 centered at the origin (0, 0) on a coordinate plane. It is widely used in trigonometry to understand the values of trigonometric functions for different angles.
To use the unit circle to evaluate trigonometric functions, follow these steps:
1. Identify the angle you want to evaluate. In this case, the angle is -3π/4.
2. Draw the angle on the unit circle. In this case, we are working with a negative angle, so we will move clockwise from the positive x-axis.
- To draw -3π/4, start by drawing a 135-degree angle, which is a quarter of a circle or π/4.
- Since we are working with a negative angle, move clockwise instead of counterclockwise. Thus, draw the angle in the third quadrant.
3. Find the point where the terminal side of the angle intersects the unit circle. The coordinates of this point will help us evaluate the trigonometric function.
- In the third quadrant, the x-coordinate is negative, and the y-coordinate is also negative.
- For -3π/4, the point of intersection will be (-√2/2, -√2/2).
4. Use the coordinates to determine the value of tangent.
- The tangent function is defined as tan(θ) = y/x, where θ is the angle and (x, y) are the coordinates.
- For -3π/4, tan(-3π/4) = (-√2/2) / (-√2/2) = 1.
Therefore, tan(-3π/4) equals 1.