simplify: (cos 32°+i sin 32°) (cos 13°+i sin 13°)
Answers
Answer:
cos(13 + 32) = cos(45) = √(2)/2
Step-by-step explanation:
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PRECALCULUS MATH HELP COLLEGE PRE CALCULUS
K w. asked • 11/30/17
Use an Addition or Subtraction Formula to find the exact value of the expression
A.) tan(− 11π/12)
B.) cos(13°) cos(32°) − sin(13°) sin(32°)
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1 Expert Answer
By:
Michael J. answered • 11/30/17
TUTOR 5 (5)
Mastery of Limits, Derivatives, and Integration Techniques
SEE TUTORS LIKE THIS
Use the angles that are on the unit circle. Then add or subtract those angles to obtain the angle given.
A)
-11π/12 = - 3π/12 - 4π/12 - 4π/12
= -π/4 - 2(π/3)
tan(-π/4 - 2π/3)
π/4 is the reference angle here. It is in the 4th quadrant because of the negative sign. You rotate this angle π/3 clockwise 2 times. After the rotation, the angle ends up in the 3rd quadrant. The value of tangent is positive in the 3rd quadrant, and tan(π/4) is 1.
tan(-11π/12) = 1
B)
This is a addition angle identity for cosine.
cos(13 + 32) = cos(45) = √(2)/2