Reciprocal trig functions
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All 8 Flashcards — Reciprocal trig functions
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Question
Define sec θ, csc θ and cot θ.
Answer
sec θ = 1/cos θ, csc θ = 1/sin θ, cot θ = 1/tan θ = cos θ/sin θ.
Question
Which basic ratio does SECANT pair with?
Answer
Cosine — sec θ = 1/cos θ (match the third letter: se-C-ant ↔ -C-osine).
Question
State the identity linking tan and sec.
Answer
1 + tan²θ = sec²θ (divide sin²+cos²=1 by cos²θ).
Question
State the identity linking cot and csc.
Answer
1 + cot²θ = csc²θ (divide sin²+cos²=1 by sin²θ).
Question
How do you solve an equation containing sec x?
Answer
Rewrite sec x = 1/cos x, take reciprocals to get cos x = …, then solve as a normal cosine equation.
Question
Where is sec θ undefined?
Answer
Wherever cos θ = 0, i.e. θ = 90°, 270°, … (π/2, 3π/2, …).
Question
If csc θ = 13/12 in Q1, find cot θ.
Answer
1 + cot²θ = (13/12)² = 169/144 ⇒ cot²θ = 25/144 ⇒ cot θ = +5/12 (Q1).
Question
Find sec(π/3).
Answer
1/cos(π/3) = 1/(1/2) = 2.
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Full study notes for Reciprocal trig functions
Topic 3.9 hub
Reciprocal & inverse trig (HL only)
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