Summary
Trigonometric functions include the reciprocal functions cosecant, secant, and cotangent, which are used alongside sine, cosine, and tangent. These functions have specific properties and graphs that are important for understanding angles of any magnitude.
- Cosecant (cosec) — the reciprocal of sine. Example: cosec(θ) = 1/sin(θ)
- Secant (sec) — the reciprocal of cosine. Example: sec(θ) = 1/cos(θ)
- Cotangent (cot) — the reciprocal of tangent. Example: cot(θ) = 1/tan(θ)
- Trigonometric identities — equations involving trigonometric functions that are true for all values of the variable. Example: sin²(θ) + cos²(θ) = 1
- Inverse trigonometric functions — functions that reverse the effect of the original trigonometric functions, defined by restricting the domain. Example: sin⁻¹(x) is the inverse of sin(x) when the domain is restricted.
Exam Tips
Key Definitions to Remember
- Cosecant is the reciprocal of sine.
- Secant is the reciprocal of cosine.
- Cotangent is the reciprocal of tangent.
Common Confusions
- Confusing the reciprocal functions with their original functions.
- Misunderstanding the domain restrictions for inverse trigonometric functions.
Typical Exam Questions
- What is the reciprocal of sine? Cosecant
- How do you express sin x + √3 cos x in the form r sin(x - α)? Use trigonometric identities to rewrite the expression.
- What are the general solutions for trigonometric equations? Use identities and algebraic manipulation to find solutions.
What Examiners Usually Test
- Understanding and application of trigonometric identities.
- Ability to graph and interpret sec, cosec, and cot functions.
- Solving equations using inverse trigonometric functions.