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Trigonometry Worksheets

What is trigonometry?

At it's most basic, trigonometry has to do with the properties of triangles. "Trigonos" is the same root used for the word triangle and means three sided, while "metry" is a suffix used to mean measurement - like in the word geometry.

Trigonometry is the study of how the side length and angles in a triangle relate to one another. Most commonly, right triangles are used. A right triangle has one angle that is 90 degrees (the same as a corner of a square). A 90 degree angle is the same as a right angle.

Although each of these triangles is different, they are all right triangles - the 90 degree angle is marked with a small square to show this.

How is trigonometry used in the real world?

Suppose you wish to know the height of a tree. Look at the following picture of the situation:

You want to find h and you know only d (the distance to the tree) and A (the angle to the top of the tree. The trigonometric relationship tan (short for tangent) will tell you the answer. The tangent of angle A is equal to h/d.

Algebra allows us to rearrange this to get an equation: tan(A) x d = h.

A basic problem using trigonometry.

If a class of ten calculus students has their IQs measured as 120, 110, 100, 99, 132, 110, 97, 105, 115, and 106, what is the average IQ in that class?

A simple average is calculated by adding up all the data points (IQs) and then dividing by the number of measurements taken. The sum of the ten IQs is 1,094 and this sum, divided by 10 equals the average, 109.4.

An interesting fact about Trigonometry.

In the above diagram, how far is it to the top of the tree from the corner where angle A is? (This is the unlabeled line, the hypotenuse of the right triangle above.)

The relationship cosine (abbreviated cos) relates d (the side of the triangle we know) to the hypotenuse, which is the distance we want to find. The relationship is given as cos(A) = d/hypotenuse. We can rearrange this so that the value we want to find is on one side of the rearranged equation: hypotenuse = d/cos(A) and get an answer directly.

Who invented trigonometry?

No one person invented trigonometry. The techniques developed in many civilizations and demonstrate how useful trigonometry is. The more advanced versions came out of India, but in the form we use it today (as ratios of side length and angles) trigonometry is of fairly modern origin.

The trigonometric functions - sine, cosine and tangent - have found use in many fields and are so practical that most calculators include keys for these functions (sin, cos, tan).

An interesting fact about trigonometry.

Trigonometry as it is usually taught depends on flat triangles. The relationships between side lengths and angles is only valid when a triangle is drawn on a flat plane. Drawing the same triangle on a sphere (or a donut) will give an incorrect answer.

This is because, on a plane surface, the interior angles of all triangles add up to 180 degrees. On other surfaces, this isn't necessarily so. On proof that the world is nearly a sphere would be to draw a triangle with one side on the equator and the other two sides going up on opposite sides of the planet.

The two lines drawn up, due north (right angles from the equator) will meet at the north pole. They will join to make a third right angle.

Although it will be huge, this triangle will violate the law that all triangles have interior angles that add up to 180 degrees. In fact, this triangle's angles will add up to 270 degrees (3 x 90 degrees).

The study of surfaces based on these types of properties is called topology and can tell us whether or not our 3-dimensional space is curved or flat, even though we cannot see it directly.

Click on the Trigonometry worksheet set you wish to view below.


  1. Absolute Value
  2. Absolute Value Equations
  3. Absolute Value Inequalities
  4. Absolute Value of Complex Numbers
  5. Adding and Subtracting Rational Expressions
  6. Addition and Subtraction of Complex Numbers
  7. Angle Sum and Difference
  8. Arc Length and Radian Measure
  9. Area of Triangle Using Trigonometry
  10. Arithmetic and Geometric Sequences and Series
  11. Binomial Theorem
  12. Central Tendency and Dispersion
  13. Co-Functions
  14. Comparison of Volumes of Similar Solids
  15. Completing the Square
  16. Composition of Functions
  17. Cosine
  18. Direct and Inverse Variation
  19. Direct Variation
  20. Division of Rational (Fractional) Expressions
  21. Equations of Circles
  22. Evaluating Rational (Fractional) Exponent
  23. Exponential Expressions and Equations
  24. Exponential Functions
  25. Factoring Polynomials
  26. Find The Missing Angle
  27. Functions - Domain and One-to-one, Onto
  28. Graphs Dealing with Sine and Cosine
  29. Graphing Complex Numbers
  30. Graphs Dealing with Tangent, Cotangent, Secant, Cosecant
  31. Graphs of Polynomial Equations of Higher Degree
  32. Graphs Of Circles
  33. Imaginary Units and Standard Complex Form
  34. Inverse Functions
  35. Inverse Trig. Functions
  36. Law of Cosines
  37. Law of Sines
  38. Law of Sines and the Ambiguous Case
  39. Length of Line Segments
  40. Linear Quadratic Systems
  41. Logarithmic Equations
  42. Logarithmic Expressions
  43. Logarithmic Functions
  44. Multiplying Rational (Fractional) Expressions
  45. Multiplying And Dividing Complex Numbers
  46. Nature of Roots
  47. Normal Distribution and Standard Deviation
  48. Polynomial Equations of A Higher Degree
  49. Positive, Negative, Zero Exponents
  50. Powers of i
  51. Trig. Proportions
  52. Pythagorean Identities
  53. Quadratic Inequalities
  54. Radical Equations
  55. Radicals
  56. Rational (Fractional) Exponent
  57. Rational Equations
  58. Rational Inequalities
  59. Rationalizing Denominators with Radicals
  60. Recognize and Evaluate Functions
  61. Recursive Sequences
  62. Reference Angles and Triangles
  63. Regression Analysis
  64. Scale Drawings
  65. Sigma Notation
  66. Simplifying Square Roots with Negative Numbers
  67. Simplify Complex Fraction Expressions
  68. Similar Polygons: Ratio of Perimeters & Areas
  69. Simplifying Rational-Fractional Expression
  70. Solving Combinations of Variations
  71. Solving Quadratic Equations
  72. Solving Quadratic Equations with Complex Roots
  73. Special Right Triangles (Geometry emphasis)
  74. Special Right Triangles (Trigonometry Emphasis)
  75. The Discriminant
  76. Transformation with Functions
  77. Trigonometric Equations
  78. Trigonometric Functions
  79. Trigonometric Ratios
  80. Trigonometric Sequences
  81. Trigonometric Word Problems
  82. Working with Right Triangles

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