Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant.

What are the trigonometric ratios?

sine, left parenthesis, angle, A, right parenthesis, equalsstart fraction, start color blueD, o, p, p, o, s, i, t, e, end color blueD, divided by, start color goldD, h, y, p, o, t, e, n, u, s, e, end color goldD, end fraction
cosine, left parenthesis, angle, A, right parenthesis, equalsstart fraction, start color purpleC, a, d, j, a, c, e, n, t, end color purpleC, divided by, start color goldD, h, y, p, o, t, e, n, u, s, e, end color goldD, end fraction
tangent, left parenthesis, angle, A, right parenthesis, equalsstart fraction, start color blueD, o, p, p, o, s, i, t, e, end color blueD, divided by, start color purpleC, a, d, j, a, c, e, n, t, end color purpleC, end fraction
cotangent, left parenthesis, angle, A, right parenthesis, equalsstart fraction, start color purpleC, a, d, j, a, c, e, n, t, end color purpleC, divided by, start color blueD, o, p, p, o, s, i, t, e, end color blueD, end fraction
sec(A)=\large\sec(\angle A)=start fraction, start color goldD, h, y, p, o, t, e, n, u, s, e, end color goldD, divided by, start color purpleC, a, d, j, a, c, e, n, t, end color purpleC, end fraction
csc(A)=\large\csc(\angle A)=start fraction, start color goldD, h, y, p, o, t, e, n, u, s, e, end color goldD, divided by, start color blueD, o, p, p, o, s, i, t, e, end color blueD, end fraction
Want to learn more about sine, cosine, and tangent? Check out this video.
Want to learn more about cotangent, secant, and cosecant? Check out this article.

Practice set 1: sine, cosine, and tangent

Problem 1.1
sine, left parenthesis, angle, B, right parenthesis, equals
  • Your answer should be
  • a proper fraction, like 1, slash, 2 or 6, slash, 10
  • a simplified proper fraction, like 3, slash, 5
  • an improper fraction, like 10, slash, 7 or 14, slash, 8
  • a simplified improper fraction, like 7, slash, 4
Use an exact expression.

Want to try more problems like this? Check out this exercise.

Practice set 2: cotangent, secant, and cosecant

Problem 2.1
cotangent, left parenthesis, angle, B, right parenthesis, equals
  • Your answer should be
  • a proper fraction, like 1, slash, 2 or 6, slash, 10
  • an improper fraction, like 10, slash, 7 or 14, slash, 8
Use an exact expression.

Want to try more problems like this? Check out this exercise.