If tanθ=3√/3 , which of the following is a possible coordinate pair? (1 point) Responses (−12,−3√2) left parenthesis negative Start Fraction 1 over 2 End Fraction comma negative Start Fraction Start Root 3 End Root over 2 End Fraction right parenthesis (−3√2,12) left parenthesis negative Start Fraction Start Root 3 End Root over 2 End Fraction comma Start Fraction 1 over 2 End Fraction right parenthesis (3√2,12) left parenthesis Start Fraction Start Root 3 End Root over 2 End Fraction comma Start Fraction 1 over 2 End Fraction right parenthesis (12,3√2)
To find the possible coordinate pairs, we need to find the values of sinθ and cosθ.
Since tanθ = sinθ / cosθ, we can let sinθ = 3√/3 and cosθ = √3/3.
To determine the signs of sinθ and cosθ, we can use the quadrant in which tanθ is positive. In this case, tanθ is positive for angles between 0 and 90 degrees, and between 180 and 270 degrees.
Since tanθ = 3√/3 is positive, we know that sinθ must also be positive. Therefore, sinθ = 3√/3.
In quadrant I, both sinθ and cosθ are positive. Therefore, we can conclude that the correct coordinate pair is (3√2, 1/2).
So the correct answer is (3√2, 1/2).