Trigonometry

Definition of Trigonometry

•  Trigonometry is the study of the relationships between the angles and the sides of a right triangle.

More about Trigonometry

• Trigonometric Functions:
  For any angle, with measure a, a point P(x, y) on its terminal side, , the trigonometric functions are as follows.
  sin a =
  cos a =
  tan a =
  csc a =
  sec a =
  cot a =           (same definition)

• Trigonometric Equation:
  If the equation contains at least one trigonometric function that is true for some but not all values of the variables then that equation is called to be trigonometric equation.
• Trigonometric Identity:
  If the equation contains a trigonometric function and is true for all the values of the variables then that equation is called to be trigonometric identity.
  Trigonometric Identities includes 3 types, Quotient identities, Reciprocal identities, and Pythagorean identities.
  Quotient Identities:  and  
  Reciprocal Identities: , , and
  Pythagorean Identities: cos² θ + sin² θ = 1, sec² θ - tan² θ = 1, csc² θ - cot² θ = 1.   

• Trigonometric Ratios                (same definition)

In ΔABC with right ∠C,

• Tangent Ratio:
  In a right angled triangle, the tangent of an angle is the ratio of the length of the side opposite to that angle to the length of the side adjacent to that angle.   

Solved Example on Trigonometry

Which of the following trigonometric ratios is the ratio between adjacent side and hypotenuse?
Choices:
A. cosine
B. tangent
C. sine
D. none of the above
Correct Answer: A
Solution:
Step 1: The ratio of adjacent side to hypotenuse is cosine.

Related Terms for Trigonometry

• Equations
• Functions
• Ratios
• Identity
• Reciprocal
• Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent