Use a half-angle formula to evaluate the following expression without using a ca
ID: 3026583 • Letter: U
Question
Use a half-angle formula to evaluate the following expression without using a calculator cos an-1) a, Let tan-1(-1)=such that tan -I. The terminal side of angle lies in aadrant Ill. b. What is the value of cos a? (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers th the expression,) c. The terminal side of the half-angle lies in Quadrant liv d. Is the cosine function positive or negative in this quadrant? The cosine function is positive in this quadrant e. Which half-angle formula should be used to evaluate the expression cos | tan-r-11 ? 1 + cos The half-angle formula l cos should be used to evaluate the expression. t. Choose the coret formula below used to evaluate the expression cos tan(-1 and completo the exg (Type an exact answer,using radicals as needed. Use integers or fractions for any numbers in the expression) OA, cos tan-1(-1)1-1 Click to select your answer(s). escExplanation / Answer
a tan alpha =-1
tan function is negative in second quadrant. SO terminal side lies in second quadrant.
opposite=1 adjacent =1
Hypotenuse=sqrt(1+1)=sqrt2
b.cos alpha=adjacent/hypotenuse =-1/sqrt2
c.The terminal side of half angle lies in first quadrant
d.Cosine is positive in this quadrant .
f. cos(alpha/2)=sqrt(1+1/sqrt2)/2 ) = sqrt((sqrt2 +1)/2sqrt2)
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