Find the values of the six trigonometric functions of θ with the given constraint. Function Value cos(θ)=16/65. Constraint θ lies in Quadrant III

Solution:

cos(θ) = base /hypotenuse and it is negative in the 3^rd quadrant

Base = 16 and hypotenuse = 65

Therefore perpendicular = √65² - 16² =  √3969 = 63

Sin(θ) = Perpendicular / Hypotenuse = -63/65 (-ve in the 3^rd quadrant)

Tan(θ) = Perpendicular/Base =  63/16(+ve in the 3^rd quadrant)

Sec(θ) = Hypotenuse/Base = -65/16(-ve in the 3^rd quadrant)

Cosec(θ) = Hypotenuse/Perpendicular = - 65/63  (-ve in the 3rd quadrant)

Cot(θ) = Base/Perpendicular = 16/63(+ve in the 3^rd quadrant)

Find the values of the six trigonometric functions of θ with the given constraint. Function Value cos(θ)=16/65. Constraint θ lies in Quadrant III

Summary:

The values of the six trigonometric functions of θ with the given constraints i.e. Function Value  cos(θ)=16/65 and θ lies in Quadrant III are Sin(θ) = -63/65 ,cos(θ)= -16/65, Tan(θ) = 63/16, Sec(θ) = -65/16, Cosec(θ) =  - 65/63, Cot(θ) = Base/Perpendicular = 16/63