Given that cosθ=−3√/2 , find the coordinates of the point where the terminal side of θ intersects the unit circle, if θ is an obtuse angle.(1 point) Responses (12,−3√2) left parenthesis 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 negative Start Fraction 1 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√)
To find the coordinates of the point where the terminal side of θ intersects the unit circle, we need to find the values of sinθ.
Since cosθ = -3√2/2, we can use the Pythagorean identity sin^2θ + cos^2θ = 1 to solve for sinθ:
sin^2θ + (-3√2/2)^2 = 1
sin^2θ + 9/4 = 1
sin^2θ = 1 - 9/4
sin^2θ = 4/4 - 9/4
sin^2θ = -5/4
Since θ is an obtuse angle, sinθ is negative. Therefore, sinθ = -√(5/4) = -√5/2.
So, the coordinates of the point where the terminal side of θ intersects the unit circle are (-√5/2, -3√2/2).
Therefore, the correct answer is (-3√2/2, -√5/2).