Module 5: Lesson 4

 

Self-Check 1

 

Questions 1.a., 1.c., 1.e., 2.a., and 2.c. on page 306 of the textbook

1.  
   1. The expression cos 43° cos 27° − sin 43° sin 27° has a similar form to the identity cos (A + B) = cos A cos B − sin A sin B. Thus, cos 43° cos 27° − sin 43° sin 27° = cos (43° + 27°) or cos 70°.

   3. The expression cos2 19° − sin2 19° is similar to the identity cos (2A) = cos2 A − sin2 A. Thus, cos2 19° − sin2 19° = cos (2 × 19°) or cos 38°.

   5. The expression  can be written as The expression inside the parentheses is of the form 2 sin A cos A, which is the part of the identity sin (2A) = 2 sin A cos A.
      
      

      Thus,
      
      

       

       

2.  

   1. The expression cos 40° cos 20° − sin 40° sin 20° has a similar form to the identity cos (A + B) = cos A cos B − sin A sin B. Thus, cos 40° cos 20° − sin 40° sin 20° = cos (40° + 20°) or cos 60°. When expressed as an exact value

   3. The expression  is similar to the identity cos (2A) = cos2 A − sin2 A. Thus, or When expressed as an exact value

© 2012 Alberta Education