The x-axis angle nearest the terminal side of angle θ is 2 π. Subtract 0 and π 4 to find the reference angle. The x-axis angle nearest the terminal side of angle θ is 0. Subtract π and 2 π 3 to find the reference angle. The x-axis angle nearest the terminal side of angle θ is π. Subtract π and 7 π 6 to find the reference angle. It is easiest to start by stetching a graph of the angle in standard position like in Figure 7. All the unit circle formulas can be similarly modified.įind the reference angle for a) 7 π 6, b) 2 π 3, c) π 4, and d) 7 π 4. Notice the last equation matches the unit circle formula with r = 1. Sin θ = y Unit Circle sin θ = opp hyp Right Triangle sin θ = y r Apply the right triangle formula for the acute angle by the origin. Figure 2: Right triangle drawn to a point on a circle.īy comparing the unit circle formulas and the right triangle formulas, we can develop the formulas for any angle. A right triangle can be drawn to the point where one acute angle is at the point, the other acute angle is at the origin, and the right angle is on the x-axis. To combine these ideas, consider a circle where r ≠ 1. In lesson 4.3 we explored right triangle trigonometry. In lesson 4.2, we looked at the unit circle. Trigonometric Functions of Angles on Circles with r ≠ 1 By combining the ideas of the unit circle and right triangles, we can describe the location of any capsule on the Eye with trigonometry. The London Eye is a farris wheel with a diameter of 394 feet. Evaluate trigonometric functions of any angle.įigure 1: London Eye.

Terminal side of theta calculator