Google Classroom
GeoGebraGeoGebra Classroom
GeoGebra

Trigonometric Ratio of General Angles

Author:Gabriel Cheow

Trigonometric Ratios in a Unit Circle

For a general angle , we will use the Cartesian coordinate system to redefine its trigonometric ratios in terms of the coordinates of P(x,y) and its distance from the origin O. In this case we will let P be a point on the circumference of a unit circle (a circle with radius of 1 unit.)

If is in the first quadrant, which of the following trigonometric ratios is/are positive?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

If is in the second quadrant, which of the following trigonometric ratios is/are positive?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

If is in the third quadrant, which of the following trigonometric ratios is/are positive?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

If is in the fourth quadrant, which of the following trigonometric ratios is/are positive?

Select all that apply
  • A
  • B
  • C
Check my answer (3)
In each of the quadrants, some trigonometric ratios are positive, some others are negative. We can summarise using the diagram above, known as ASTC diagram. Note: We can only use the ASTC diagram to determine the signs of if .

ASTC Diagram

ASTC Diagram

New Resources

Discover Resources

Discover Topics