Trig Unit Unit Circle Lesson

Each of the 4 quarters of a circle

• Quadrants of a circle are numbered

  going counter clockwise​

• The quadrant determines whether

  the x and y values are positive

  or negative​

The triangle at the right is a right triangle, and θ is in standard position.

• to evaluate sine and cosine, we use the coordinates that lie on the Unit Circle's circumference

• cosine of an angle is equal to the length of the reference triangle's adjacent side and is represented by the x-coordinate

• sine of an angle is equal to the length of the reference triangle's opposite side and is represented by the y-coordinate

• Sin(angle) = y-coordinate of point

• Sine is positive in the FIRST and SECOND quadrants.

• Sine is negative in the THIRD and FOURTH quadrants.

• sin(135°) = √2/2

• sin(4π/3) = -√3/2

• sin(0) = 0

• Cos(angle) = x-coordinate of point

• Cosine is positive in the FIRST and FOURTH quadrants.

• Cosine is negative in the SECOND and THIRD quadrants.

• cos(2π/3) = -1/2

• cos(270°) = 0

• cos(π/6) = √3/2

• Tan(angle) = y-coordinate/x-coordinate

• Tangent is positive in the FIRST and THIRD quadrants.

• Tangent is negative in the SECOND and FOURTH quadrants.

• tan(90°) = 1/0 = UNDEFINED

• tan(π) = 0/-1 = 0

• tan(240°) = (-√3/2)/(-1/2)

• =(-√3/2) *(-2/1) = √3/1 = √3