• 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

Using the Value of One Trig Function to Find Another

If the value of one trig function is known, any of the other trig functions can be calculated.

Example

Suppose α = tan θ is known.

This situation can be represented by the following diagram. We set the adjacent side to length 1.  Then using the definition of tangent, the opposite side must have length tan θ, thar is, α.

Using Pythagoras Theorem we find the hypotenuse is of length . Each of the three sides are now determined and

and .

Exercise 4

Suppose α = sin θ is known. Find tan θ and cos θ in terms of α.

Answer

Exercise 5

Suppose α = cos θ is known. Find tan θ and sin θ in terms of α.

Answer

<< Trigonometric Identities  | Trigonometry Index | Measuring Angles (Degrees and Radians)>>