Determine tanx if secx=(sqrt14)/2 and is in the second quadrant

Nov 2008
425
0
Can someone explain this to me please?

Determine tanx if secx=(sqrt14)/2 and is in the second quadrant

How would I approach this because I am confused about the sqrt14 and when I did get tan, it was -0.098etc. or something with that.. if it's negative and decimals, can tanx be correct?
 
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pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
Can someone explain this to me please?

Determine tanx if secx=(sqrt14)/2 and is in the second quadrant

How would I approach this because I am confused about the sqrt14 and when I did get tan, it was -0.098etc. or something with that.. if it's negative and decimals, can tanx be correct?
I would say if sec(x) = sqrt(14)/2 then cos(x) = 2/sqrt(14)

The Six Trigonometric Functions

From here you can use sin^2(x)+cos^2(x) = 1

Subbing in for cos(x) and solving for sin(x) you will get

sin(x) = sqrt(8)/sqrt(14)

Now use tan(x) = sin(x)/cos(x)

This should give tan(x) = sqrt(2), thisanswer is in the 1st quadrant.

tan is negative in the 2nd quadrant so tan(x) = -sqrt(2)