Find the six trigonometric functions of θ given that

Question

cos θ = −1/2 and sin θ > 0.?

Answer 1

cos(θ) = - 1/2

cos(θ) = Adjacent side/Hypotenuse

Adjacent side = 1, Hypotenuse = 2

From the pythagorean theorem,

Opposite side = √[(Hypotenuse)² - (Adjacent side)²] 

                           = √[(2)² - (1)² ]

                          = √(4 - 1)

                          = √3

cos(θ) is negative and sin(θ) is positive in second quadrant.

sin(θ) = Opposite side / Hypotenuse

         = √3/2

tan(θ) = Opposite side/Adjacent side

          = - √3/1

cot(θ) = Adjacent side/Opposite side

          = - 2/√3

cosec(θ) =  Hypotenuse/Opposite side

              = 2/√3

sec(θ) = Hypotenuse/Adjacent side

          = - 2/1

sin(θ) = √3/2 , tan(θ) = - √3, cot(θ) = - 2/√3, cosec(θ) = 2/√3, sec(θ) = - 2.