#### Read Microsoft Word - TrigIdentitiesI.doc text version

`Trigonometric Identities WorksheetGiven: Fundamental Identitiessin  cos 1 csc = sin  2 sin  + cos 2  = 1 tan =cos sin  1 sec = cos 2 tan  + 1 = sec 2  cot  =1 tan  2 1 + cot  = csc 2  cot  =Establish (or verify) the following identities. 1.1 ­ tan  cot  ­ 1 = 1 + tan  cot  + 12.cos2 x = 1 ­ sin x 1 + sin x3.tan  sin  = sec  ­ cos 4.sin  1 + cos  + = 2 csc  1 + cos  sin 5.4 If tan  = ­ , 3 1 &lt;  &lt;  and cos  = ­ , 2 2&lt; &lt;3 , find the exact value of: 2(a) sin ( +  )(b) tan ( +  )6.Use the given angle sum and difference identities to verify the following identities: cos (A + B) = cos A cos B ­ sin A sin B and cos (A ­ B) = cos A cos B + sin A sin B  (a) cos  ­   = sin  2 (b) cos (  +  ) = ­cos 7.Use the angle sum identity sin (A + B) = sin A cos B + cos A sin B and sin (A ­ B) = sin A cos B ­ cos A sin B to verify the following identities:  (a) sin  ­   = cos  2 (b) sin (  ­  ) = sin 8.Use one of the Half-Angle formulas to find the exact value of (a) cos 15° (b) tan    12 9.If cos  = (a) sin ( 2 )4  and 0 &lt;  &lt; , find the exact value of 5 2(b) cos ( 2 )(c) the quadrant in which 2 lies`

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##### Microsoft Word - TrigIdentitiesI.doc

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