Question 852378
If sin x<0 and tan x=-4/5, find the exact value of sec x
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reference angle in Q4 in which sin<0, cos>0, tan<0
Identity: {{{sec(x)=sqrt(1+tan^2(x))=sqrt(1+(16/25))=sqrt(41/25)=sqrt(41)/5}}}
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calculator check:
tanx=-4/5 (in Q4)
x&#8776;321.34&#730;
secx=1/cosx=1/cos(321.34)&#8776;1.2806…
Exact value=&#8730;41/5&#8776;1.2806…