SOLUTION: If sin(x) = -3/5 with x in quadrant IV, find the sec(x)

Question 773411: If sin(x) = -3/5 with x in quadrant IV, find the sec(x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

sin(x) = -3/5

sin^2(x) = (-3/5)^2

sin^2(x) = 9/25

-1*sin^2(x) = -1*9/25

-sin^2(x) = -9/25

-sin^2(x) + 1 = -9/25 + 1

-sin^2(x) + 1 = -9/25 + 25/25

-sin^2(x) + 1 = 16/25

1-sin^2(x) = 16/25

cos^2(x) = 16/25

cos(x) = sqrt(16/25) ... note: cos(x) > 0 since we're in quadrant IV

cos(x) = 4/5

1/cos(x) = 1/(4/5)

1/cos(x) = 5/4

sec(x) = 5/4

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