# lecture2 - tions if ± is in Quadrant II and sin ± = 3 5 6...

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Lecture 2: Trigonometry Appendix D ± radians = degrees 1 degree = radians 1 radian = degrees ex. Express 36 ± in radians. ex. Express 5 ± 6 radians as degrees. Arc Length ( ² in radians)

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Trigonometric Functions 6 - ? ± sin ± csc ± cos ± sec ± tan ± cot ± NOTE: ± is measured in
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 . De±ne 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 ± = Recall two basic triangles:

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Know the exact values of the trig functions for 0, ± 6 , ± 4 , ± 3 , ± 2 and ± (see tables in text or student guide) and use them to ±nd other angle values. ex. Find the exact value of cos 5 ± 6 . ex. Solve for ² in [0 ; 2 ± ) if sin ² = ± 1 p 2 .
ex. Find the values of the other trigonometric func-

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Unformatted text preview: tions if ± is in Quadrant II and sin ± = 3 5 . 6-? ± Trigonometric Identities 1) sin 2 ± + cos 2 ± = 2) tan 2 ± + 1 = 3) 1 + cot 2 ± = 4) sin( ± ± ) = 5) cos( ± ± ) = NOTE: ² sin x ² ² cos x ² 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 ± and ² are in the ±rst quadrant and sin ± = 2 3 and cos ² = 4 5 ±nd the exact value of sin( ± + ² ). ex. Solve for ± in [0 ; 2 ² ) if p 3 sin 2 ± ± 2 sin 2 ± = 0. ex. Solve for ± in [0 ; 2 ² ) where sin ± > tan ± . The Six Basic Trigonometric Graphs 6-? ± 6-? ± 6-? ± 6-? ± 6-? ± 6-? ±...
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lecture2 - tions if ± is in Quadrant II and sin ± = 3 5 6...

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