Question 820437
In each case, find sin(a), cos(a), csc(a), sec(a), and cot(a). Note: 'a' means alpha.45. cos(2a)=3/5 and 0°<2a<90°
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use cos half-angle formula:{{{cos(s/2)=sqrt((1+cos(s))/2)}}}
{{{cos(a)=cos(2a/2)=sqrt((1+cos(2a))/2)=sqrt((1+(3/5))/2))}}}
{{{sqrt((8/5)/2)=sqrt((8/10))=sqrt((4/5))}}}=2/&#8730;5=2&#8730;5/5
sin(a)=&#8730;(1-cos^2(a))=&#8730;(1-4/5)=&#8730;(1/5)=1/&#8730;5=&#8730;5/5
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sin(a)=&#8730;5/5
csc(a)=&#8730;5
cos(a)=2&#8730;5/5
sec(a)=&#8730;5/2
cot(a)=cos(a)/sin(a)=2/1=2
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calculator check:
cos(2a)=3/5
2a&#8776;53.13&#730;
a&#8776;26.565&#730;
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sin(a)=sin(26.565)&#8776;0.4472..
exact value as calculated=&#8730;5/5&#8776;0.4472..
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cos(a)=cos(26.565)&#8776;0.8944..
exact value as calculated=2&#8730;5/5&#8776;0.8944..