Unit Circle
Introduction
Introduction
The unit circle is used to extend the trigonometric function for angles beyond 90°. We can divide a unit circle into 4 quadrants.
The unit circle is used to extend the trigonometric function for angles beyond 90°. We can divide a unit circle into 4 quadrants.
In the 1st (0°< θ <90°), all ratios are positive.
In the 1st (0°< θ <90°), all ratios are positive.
In the 2nd (90°< θ <180°), only sin is positive.
In the 2nd (90°< θ <180°), only sin is positive.
In the 3rd (180°< θ <270°), only tan is positive.
In the 3rd (180°< θ <270°), only tan is positive.
In the 4th (270°< θ <360°), only cos is positive.
In the 4th (270°< θ <360°), only cos is positive.
Explore!
Explore!
Use the applet below to observe how the trigonometric function of an angle in each of the quadrants has the same magnitude as the angle of a congruent triangle in the 1st quadrant (Reference Angle / Basic Angle).
Use the applet below to observe how the trigonometric function of an angle in each of the quadrants has the same magnitude as the angle of a congruent triangle in the 1st quadrant (Reference Angle / Basic Angle).
Depending on the quadrant, the sign of the trigonometric ratio changes. Use the applet below by moving the Red Dot on the circle to change the value of the angle and observe how:
Depending on the quadrant, the sign of the trigonometric ratio changes. Use the applet below by moving the Red Dot on the circle to change the value of the angle and observe how:
- The sign of the height and base changes.
- The sign of the trigonometric changes when compared to the reference angle.
Explore!
Explore!
Use the applet below to explore how the unit circle extends the trigonometric function for angles beyond 90°.
Use the applet below to explore how the unit circle extends the trigonometric function for angles beyond 90°.
Move the Blue Dot on the Circle on the left to change the angle and observe how the blue segment in the circle corresponds to the value of the corresponding trigonometric ratio.
Move the Blue Dot on the Circle on the left to change the angle and observe how the blue segment in the circle corresponds to the value of the corresponding trigonometric ratio.
Extension
Extension
Using a circle with a radius of 1 unit, it is possible to generate the graphs of all 6 trigonometric ratios.
Using a circle with a radius of 1 unit, it is possible to generate the graphs of all 6 trigonometric ratios.
See the Instagram Post on the right.
See the Instagram Post on the right.