Right Angled Triangle
AnglesAngles (such as the angle "θ" above) can be in Degrees or Radians. Here are some examples:
"Sine, Cosine and Tangent"The three most common functions in trigonometry are Sine, Cosine and Tangent. You will use them a lot! They are simply one side of a triangle divided by another. For any angle "θ":
Sine, Cosine and Tangent are often abbreivated to sin, cos and tan.
Repeating PatternBecause the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation. When you need to calculate the function for an angle larger than a full rotation of 2π (360°) just subtract as many full rotations as you need to bring it back below 2π (360°): Example: what is the cosine of 370°? 370° is greater than 360° so let us subtract 360° 370° - 360° = 10° cos(10°) = 0.985 (to 3 decimal places) Likewise if the angle is less than zero, just add full rotations. Example: what is the sine of -3 radians? -3 is less than 0 so let us add 2π radians -3 + 2π = -3 + 6.283 = 3.283 radians sin(3.283) = -0.141 (to 3 decimal places) Solving TrianglesA big part of Trigonometry is Solving Triangles. By "solving" I mean finding missing sides and angles. Example: Find the Missing Angle "C"
It's easy to find angle C by using angles of a triangle add to 180°: So C = 180° - 76° - 34° = 70°
It is also possible to find missing side lengths and more. The general rule is: If you know any 3 of the sides or angles you can find the other 3 See Solving Triangles for more details. Other Functions (Cotangent, Secant, Cosecant)Similar to Sine, Cosine and Tangent, there are three other trigonometric functions which are made by dividing one side by another:
Trigonometric and Triangle Identities
Enjoy becoming a triangle expert! |