8 reciprocal functions another way to look at it sin

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8 Reciprocal Functions Another way to look at it… sin θ = 1/csc θ csc θ = 1/sin θ cos θ = 1/sec θ sec θ = 1/cos θ tan θ = 1/cot θ cot θ = 1/tan θ
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9 Calculate the trigonometric functions for θ . The six trig ratios are 4 3 5 θ sin = 5 4 tan = 3 4 sec = 3 5 cos = 5 3 cot = 4 3 csc = 4 5 α cos α = 5 4 sin α = 5 3 cot α = 3 4 tan α = 4 3 csc α = 3 5 sec α = 4 5 What is the relationship of α and θ? They are complementary, or α = 90 - θ Calculate the trigonometric functions for α .
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10 Note : These functions of the complements are called cofunctions. Note sin θ = cos(90 - θ ), for 0 < θ < 90 Note that θ and 90 - θ are complementary angles. Side a is opposite θ and also adjacent to 90 θ . a hyp b θ 90 θ sin θ = and cos (90 - θ ) = . So, sin θ = cos (90 - θ ) . b a b a
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11 Cofunctions sin θ = cos(90 - θ ) cos θ = sin(90 - θ ) sin θ = cos (π/2 - θ ) cos θ = sin (π/2 - θ ) tan θ = cot(90 - θ ) cot θ = tan(90 - θ ) tan θ = cot (π/2 - θ ) cot θ = tan (π/2 - θ ) sec θ = csc(90 - θ ) csc θ = sec(90 - θ ) sec θ = csc (π/2 - θ ) csc θ = sec (π/2 - θ )
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12 Trigonometric Identities are trigonometric equations that hold for all values of the variables. We will learn many Trigonometric Identities and use them to simplify and solve problems.
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13 Quotient Identities sin = cos = tan = hyp adj adj opp hyp opp opp adj hyp θ θ θ θ tan cos sin = = = = adj opp adj hyp hyp opp hyp adj hyp opp The same argument can be made for cot… since it is the reciprical function of tan.
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14 Quotient Identities tan θ = sin θ /cos θ cot θ = cos θ /sin θ
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15 Let’s look at the trigonometric functions a few familiar triangles…
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