Relationships between trig functions
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Flip to reveal answersWhat is sec θ?
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All 8 Flashcards — Relationships between trig functions
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Question
What is sec θ?
Answer
sec θ = 1/cos θ (the reciprocal of cosine).
Question
What is csc θ (cosec θ)?
Answer
csc θ = 1/sin θ (the reciprocal of sine).
Question
What is cot θ?
Answer
cot θ = 1/tan θ = cos θ / sin θ (the reciprocal of tangent).
Question
State the three Pythagorean identities.
Answer
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = csc²θ.
Question
How do you derive 1 + tan²θ = sec²θ?
Answer
Divide sin²θ + cos²θ = 1 throughout by cos²θ.
Question
How do you derive 1 + cot²θ = csc²θ?
Answer
Divide sin²θ + cos²θ = 1 throughout by sin²θ.
Question
What is the co-function relationship sin(90° − θ)?
Answer
sin(90° − θ) = cos θ (and cos(90° − θ) = sin θ).
Question
Best first step when a trig expression won't simplify?
Answer
Rewrite everything in sin and cos, combine over a common denominator, then use sin²+cos²=1.
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Full study notes for Relationships between trig functions
Topic 3.11 hub
Trig relationships (HL only)
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