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Question
Find the other trigonometric functions if sec A = `-25/7` and A lies in the second quadrant.
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Solution
Given, sec A = `-25/7`
We know that,
tan2A = sec2A – 1
= `(-25/7)^2-1`
= `625/49-1`
tan2A = `576/49`
∴ tan A = `+- 24/7` ...[Taking square root on both sides]
Since A lies in the 2nd quadrant,
tan A < 0
∴ tan A = `-24/7`
∴ cot A = `1/tan "A" = 1/((-24/7)) = -7/24`
∴ cos A = `1/sec"A" = 1/((-25/7)) = -7/25`
∴ tan A = `sin"A"/cos"A"`
∴ sin A = tan A cos A = `-24/7 xx - 7/25 = 24/25`
∴ cosec A = `1/sin"A" = 1/(24/25) = 25/24`
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