Maths Extension 1 Year 11 - Module 3 - Lesson 2
Reciprocal Trigonometric Functions
Name
Date
Class
1. Lesson focus
Reciprocal trigonometric functions. sec x=1/cos x, csc x=1/sin x and cot x=1/tan x where each denominator is non-zero.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Find csc(5π/6).
3. If tan θ=−3/4 and θ is in quadrant II, find sin θ, cos θ and sec θ.
3. Challenge
State the excluded x-values for y=sec x on 0≤x<2π.
4. Multiple choice
Which identity is valid wherever tan x is defined?
A. 1+cot²x=csc²x
B. 1+tan²x=sec²x
C. sin²x+tan²x=1
D. sec²x−1=sin²x
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Find sec(π/3).
cos(π/3)=1/2, so sec(π/3)=2.
2. Find csc(5π/6).
sin(5π/6)=1/2, so csc(5π/6)=2.
3. If tan θ=−3/4 and θ is in quadrant II, find sin θ, cos θ and sec θ.
A 3–4–5 triangle gives sinθ=3/5 and cosθ=−4/5; hence secθ=−5/4.
Challenge. State the excluded x-values for y=sec x on 0≤x<2π.
sec x is undefined when cosx=0, so x=π/2 and 3π/2 are excluded.
Multiple choice. Which identity is valid wherever tan x is defined?
Correct answer: B. Divide sin²x+cos²x=1 by cos²x to obtain tan²x+1=sec²x.
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