lecture2 - tions if ± is in Quadrant II and sin ± = 4 5 6...

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Lecture 2: Trigonometry Arc Length and Radians radians = degrees 1 = radians 1 radian = degrees ex. Express 36 in radians. ex. Find the length of an arc of a circle with radius 12 cm which is subtended by a central angle ± = 7 6 . What is the area of the corresponding sector of the circle?
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Trigonometric Functions 6 - ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ± 6 - ? ² sin ± csc ± cos ± sec ± tan ± cot ± NOTE: ± is measured in
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6 - ? ± In general, let P ( x;y ) be any point on the terminal side of ± (radians) and let r = p x 2 + y 2 be the distance from the origin to point P . Deflne sin ± = y r , cos ± = x r , and tan ± = y x . NOTE: x = r cos ± , y = r sin ± , x 2 + y 2 = r 2 . From that we can prove the basic trig identity cos 2 ± + sin 2 ± = Unit Circle
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Recall two basic triangles: 6 - ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ± 6 - ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ± Know the exact values of the trig functions for 0, 6 , 4 , 3 , 2 and (see table in student guide) and use them to flnd other angle values. ex. Find the exact value of cos 7 6 .
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ex. Solve for ± in [0 ; 2 ) if csc ± = ¡ 2 p 3 . ex. Find the values of the other trigonometric func-
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Unformatted text preview: tions if ± is in Quadrant II and sin ± = 4 5 . 6-? ± Trigonometric Identities 6-? ± 1) sin 2 ± + cos 2 ± = 2) tan 2 ± + 1 = 3) 1 + cot 2 ± = 4) sin( ¡ ± ) = 5) cos( ¡ ± ) = NOTE: • sin x • • cos x • 6) sin( x § y ) = 7) cos( x § y ) = 8) tan( x § y ) = 9) sin(2 x ) = 10) cos(2 x ) = 11) cos 2 x = 12) sin 2 x = ex. If fi and fl are in the flrst quadrant, tan fi = 2 and cos fl = 3 5 flnd the exact value of sin( fi + fl ). 6-¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ± 6-¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡± ex. Solve for ± in [0 ; 2 … ) if p 3 sin 2 ± ¡ 2 sin 2 ± = 0. ex. Solve for ± in [0 ; 2 … ) where sin ± > tan ± . The Six Basic Trigonometric Graphs y = sin x y = cos x y = tan x y = cot x y = sec x y = csc x...
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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lecture2 - tions if ± is in Quadrant II and sin ± = 4 5 6...

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