Question

what is sin(theta)= when cos(theta)= -2/3 and is in Quadrant III?

Answer 1

Answer:

-root 5÷ 3

Step-by-step explanation:

by astc rule

tan and cot are +ve in 3 quadrant

so,sin is -ve

and by applying pythagoras theorem

we calculate opposite side value

Answer 2

Answer:

sin∅ = -√5/3

Step-by-step explanation:

sin²∅ + cos²∅ = 1

sin²∅ = 1 - cos²∅

sin∅ = √ ( 1 - cos²∅ )

sin∅ = √ { 1 - ( - 2/3 )² } [ Putting the value of cos∅ = - 2/3 ]

sin∅ = √ ( 1 - 4/9 )

sin∅ = √ (5/9)

sin∅ = √5/3

sin∅ = -√5/3 [ °•° ∅ is in 3rd quadrent ]