QR ADA 2009 question

[299678]

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Which of the following is equal to cos x if sec x = -5/3 and if pie/2<x<3pie/4?
a)-0.28
b)-0.6
c) 8/5
d)7/25
e)16/25

My answer for this question was positive 0.6 I don't understand why answer should be negative. It occur in the second quadrant, so should be negative, but the value of x already has a negative, so should be positive? I don't know frustrating.

 

[hausee]

Which of the following is equal to cos x if sec x = -5/3 and if pie/2<x<3pie/4?
a)-0.28
b)-0.6
c) 8/5
d)7/25
e)16/25

My answer for this question was positive 0.6 I don't understand why answer should be negative. It occur in the second quadrant, so should be negative, but the value of x already has a negative, so should be positive? I don't know frustrating.

sec x=1/cos x=-5/3

so cos x = -3/5 = -0.6

I'm not sure we need the 0<"pie/2<x<3pie/4" here...plus x is not negative as you mentioned .

 

[lala05]

Which of the following is equal to cos x if sec x = -5/3 and if pie/2<x<3pie/4?
a)-0.28
b)-0.6
c) 8/5
d)7/25
e)16/25

My answer for this question was positive 0.6 I don't understand why answer should be negative. It occur in the second quadrant, so should be negative, but the value of x already has a negative, so should be positive? I don't know frustrating.

Cos and sec are reciprocals, so they always have the same sign. Since we are given that sec is negative, we know cos will be negative also. And like you said, pi/2<x<3pi/4 falls in the second quadrant, where cos is always negative. You can disregard the x in the calculation (except when determining the quadrant) since we're not trying to find the value of the angle (x), rather the value of its functions (cos and sec).