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Trigonometry Section 8.4 Simplify trigonometric expressions Reciprocal Relationships sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Ratio Relationships tan Θ = cot Θ =
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Cofunction Relationships sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) examples sin 30 o = sec 50 o = cot 10 o = sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ Pythagorean Relationships
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sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ sin Θ = cos Θ = tan Θ = tan θ = csc Θ = sec Θ = cot Θ = cot θ = Simplify the following expression. 1 + tan 2 (90 o – x) To simplify trig expressions 1. Look for Pythagorean Relationships 2. Look for Cofunction Relationships 3. Convert to sine and cosine
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sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ sin Θ = cos Θ = tan Θ = tan θ = csc Θ = sec Θ = cot Θ = cot θ = Simplify the following expression. sin A sec A cot A
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sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Simplify the following expression. sec Θ – sinΘ tanΘ
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sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Simplify the following expression. csc B (cos 3 B tan B – sin B)
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sin Θ= cos(90 o – Θ) sec Θ= csc(90 o – Θ) tan Θ= cot(90 o – Θ) cos Θ= sin(90 o – Θ) csc Θ= sec(90 o – Θ) cot Θ= tan(90 o – Θ) sin 2 Θ + cos 2 Θ = 1 1 + tan 2 Θ = sec 2 Θ 1 + cot 2 Θ = csc 2 Θ sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Prove the identity. sin A + cos A = sin A csc A csc A sec A
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Assignment Page 321 Problems 2 – 22 even, 30,32,34
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