Find the exact value of each of the remaining trigonometric

Find the exact value of each of the remaining trigonometric functions of theta. sec theta = -19, tan theta > 0.

Solution

given that sec(theta) = -19, tan(theta) >0

ie tan(theta) = +Ve and sec(theta) , cos(theta) ( = 1/sec(theta)) = - ve ,which indicates that theta lies in third quadrant.

cos(theta) = 1/sec(theta)

= - 1/19

sin(theta) = +- ( 1-cos²(theta))^1/2

= +- ( 1- ( -1/19)²) ^1/2

sin(theta) = - 1.00 ( sin is -Ve in third quadrant)

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tan(theta) = sin(theta) / cos(theta)

= - 1 / (- 1/19)

= 19

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cosec (theta) = 1/sin (theta)

= - 1

cot(theta) = 1/ tan(theta)

= 1/19