The unit circle: using cosθ and sinθ as the x- and y
The key idea with triangles who's hypotenuse lie on the unit circle (that form an angle of θ with the x-axis) is that cosθ represents length of the base, and sinθ represents the height.
Take a look at the graph below and notice the following relationships always hold:
The following table shows the values of sinθ and cosθ for the so called critical angles θ. These are angles that give "nice" values for sin and cos:
The unit circle can be divided into quadrants based on the sign of cosθ and sinθ. These correspond to the 4 quadrants produced by the intersection of the x and y axes. The quadrants are denoted Q1, Q2, Q3 and Q4.
Since a full circle is 2π radians, adding 2π to any angle θ gives the same point on the unit circle. In fact, adding any integer multiple of 2π gives the same point:
Nice work completing The Unit Circle, here's a quick recap of what we covered:
Exercises checked off
The unit circle: using cosθ and sinθ as the x- and y
The key idea with triangles who's hypotenuse lie on the unit circle (that form an angle of θ with the x-axis) is that cosθ represents length of the base, and sinθ represents the height.
Take a look at the graph below and notice the following relationships always hold:
The following table shows the values of sinθ and cosθ for the so called critical angles θ. These are angles that give "nice" values for sin and cos:
The unit circle can be divided into quadrants based on the sign of cosθ and sinθ. These correspond to the 4 quadrants produced by the intersection of the x and y axes. The quadrants are denoted Q1, Q2, Q3 and Q4.
Since a full circle is 2π radians, adding 2π to any angle θ gives the same point on the unit circle. In fact, adding any integer multiple of 2π gives the same point:
Nice work completing The Unit Circle, here's a quick recap of what we covered:
Exercises checked off