mac1147_lecture18_1_b

mac1147_lecture18_1_b - L18 Unit Circle Approach;...

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250 L18 Unit Circle Approach; Properties of the Trigonometric Functions; Graphs of Sine and Cosine Functions Let ( , ) P xy = be a point on the Unit Circle that corresponds to the angle θ in standard position. Since 1 r = , the six trigonometric functions of the angle are: sin y = tan y x θ= , 0 x 1 csc y = , 0 y cos x cot x y = , 0 y 1 sec x , 0 x If is measured in radians, then the length of the arc of the unit circle subtended by the angle is 1 s =⋅ . Then, = s units of length 1 unit of length Therefore, angle expressed in radians has no dimension , that is, is a real number. Thus, in the table above, we defined the six trigonometric functions of a real number - angle expressed in radians .
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251 Example : Let ( , ) P xy = be a point on the Unit Circle with 1 2 x =− and 3 2 y = . Find the six trigonometric functions of the corresponding angle θ ( 02 π ≤< ).
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252 Domains of the Trigonometric Functions For sin y θ = and cos x θ= : tan y x = and 1 sec x = : cot x y and 1 csc y :
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253 Ranges of the Trigonometric Functions For a point ( , ) P xy = on the Unit Circle, 1 x and 1 y that is, 11 x −≤ ≤ and 1 1 y ≤≤ Since
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mac1147_lecture18_1_b - L18 Unit Circle Approach;...

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