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PP Section 6.2

# PP Section 6.2 - the terminal side of the angle Find the...

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Trigonometric Functions of  Angles

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The unit circle is a circle whose radius is 1 and whose center is at the origin. Since r = 1: s r = θ becomes s = θ
(0, 1) (-1, 0) (0, -1) (1, 0) s = θ θ y x

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Let θ be an angle in standard position and let P = ( a , b ) be the point on the unit circle that lies on the terminal side of θ . The sine function associates with θ the y -coordinate of P and is denoted by b = θ sin The cosine function associates with θ the x -coordinate of P and is denoted by a = θ cos
The tangent function is denoted by tan θ and it is defined as 0 , tan = a a b θ The cotangent function is denoted by cot θ and it is defined as 0 , cot = b b a θ

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The secant function is denoted by sec θ and it is defined as 0 , 1 sec = a a θ The cosecant function is denoted by csc θ and it is defined as 0 , 1 csc = b b θ
(0, 1) (-1, 0) (0, -1) (1, 0) θ = t θ y x P = ( a , b ) sin  = b θ cos  = a θ tan  = b/a θ cot  = a/b θ sec  = 1/a θ csc  = 1/b θ

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( 29 - = = 4 15 , 4 1 , b a P 4 15 sin - = = b θ 4 1 cos = = a θ Let θ be an angle in standard position, and let P

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Unformatted text preview: the terminal side of the angle. Find the value of the trigonometric functions of θ. 15 4 1 4 15 tan-=-= = a b θ ( 29 -= 4 15 , 4 1 , b a 15 15 15 1 4 15 4 1 cot-=-=-= = b a 4 4 1 1 1 sec = = = a θ 15 15 4 15 4 4 15 1 1 csc-=-=-= = b ( 29 -= 4 15 , 4 1 , b a (0, 1) (-1, 0) (0, -1) (1, 0) y x Give the value of the trigonometric functions of the quadrantal angles. Use a calculator to find the approximate value of (a) sin52 b tan 5 (c) o ( ) sec π 5 Using a Calculator Set the Correct Mode Before using your calculator make sure that the right mode (degrees or radians) is selected. 236068 . 1 cos 1 sec 7265426 . tan 788011 . 52 sin 5 5 5 = = = = π o...
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