• MathsFirst Home
• Online Maths Help
  • Notation
  • Arithmetic
    • Decimals
    • Fractions
    • HCF and LCM
    • Order of Operations
    • Signed Numbers
  • Algebra
    • Exponents
      • Integer Exponents
      • Fractional Exponents
      • Exponents Worksheet
    • Combining Like Terms
    • Simple Expansions
    • Factorisation
    • Mathematical Formulae
      • Constructing Formulae
      • Rearranging Formulae
        • Order of Operations for Algebraic Expressions
        • Inverse Operations and Functions
        • Rearranging Equations I (Simple Equations)
        • Rearranging Equations II (Quadratic Equations)
        • Rearranging Equations III (Harder Examples)
      • Area, Surface Area and Volume Formulae
    • Coordinate Systems and Graphs
    • Linear Equations & Graphs
    • Simultaneous Linear Equations
    • Polynomials
    • Quadratic Polynomials
    • Rational Functions
    • Logarithms
  • Calculus
    • Differentiation
      • Tangents, Derivatives and Differentiation
      • The Basic Rules
      • Products and Quotients
      • Chain Rule
      • Logarithmic Differentiation
      • Mixed Differentiation Problems
      • Sign of the Derivative
      • Sign of the Second Derivative
    • Integration
      • Basic Integrals
      • Multiple, Sum and Difference Rules
      • Linear Substitution
      • Simpler Integration by Substitution
      • Harder Integration by Substitution
      • Trig Substitution 1
      • Trig Substitution 2
      • Integration by Parts
  • Trigonometry
    • Pythagoras Theorem
    • Trig Functions and Related Topics
• First Year Maths Pathways
• Readiness Quizzes
• Study Maths
  at Massey
  • Undergraduate
  • Postgraduate
• Other Math Links
• About MathsFirst
• Contact Us

Trigonometry

Calculators and Trigonometric Functions

Calculators can be used to compute the values of trig functions at angles that are not necessarily special ( 0º, 30º = π/6, 45º = π/4, 60º = π/6, 90º = π/2).

Always make sure your calculator is set at the right mode (DEG or RAD)

Note: On some scientific calculators, to obtain the value of π you press the π key. On others, you press the EXP. Before continuing on, test your calculator to find which key gives you the value of π = 3.14159265359…

Exercise

Exercise

Note that for any x,

If you are given the value of a trig function you can find the angle by using the inverse of the trig function.

gives a value θ in such that

gives a value θ in such that

gives a value θ in such that

Example

Find θ between and π so that sin θ = 0.3

By a calculator,

This is in the first quadrant:

To get the value in the second quadrant we calculate θ = π – 0.3047 =2.837   

Exercise 6.

<< Trigonometry Functions on General Angles | Trigonometry Index | Graphs of Trig Functions >>