TRIGONOMETRY 1

Express each of the following as trigonometric ratios of positive acute angles: (i)  Sin(-50⁰)  (ii) Cos(-210⁰)   (iii) Tan( -170⁰)

Solution

i)   Sin(-50⁰)  = Sin (360⁰-50⁰)

                      = Sin 310⁰

Sin θ = -Sin(360⁰- θ)  [since it is in the 4^th quadrant]

Sin 310⁰ = -Sin(360⁰- 310⁰)

               =  -Sin 50⁰ 

ii)   Cos(-210⁰)  = Cos (360⁰-210⁰)

                           = Cos 150⁰

Cos θ = -Cos(180⁰- θ)  [since it is in the 2nd quadrant]

Cos 150⁰ = -Cos(180⁰- 150⁰)

                =  -Cos 30⁰ 

ii)   Tan(-170⁰)  = Tan (360⁰-170⁰)

                           = Tan 190⁰

Tan θ = -Tan(θ - 180⁰)  [since it is in the 3rd quadrant]  

Tan 190⁰ = -Tan(190⁰- 180⁰)

                =  -Tan 10⁰ 

TRY THIS………

Express each of the following as trigonometric ratios of positive acute angles.

(i)  Sin(-60⁰)  (ii) Cos(-280⁰)   (iii) Tan( -130⁰)