On the unit circle, (x,y) = (cos(240), sin(240) ) = (-sqrt(3) / 2, -1/2)
C: -1/2 (x coordinate) and A: – ∛3 / 2 (y coordinate) Explanation: 1) On the unit circle, the x and y coordinates are the cosine and sine ratios respectively. 2) 600° corresponds to 600 – 360° = 240°. 3) 180° < 240° < 270° ⇒ the point is in the third quadrant. Third quadrant ⇒ x and y coordinates are negative, so D. cannot be a solution. 4) You can work with the extra angle to use notable angles: 240° - 180° = 60° The sine and cosine of 60° are known: sin 60° = ∛3 / 2, and cos 60° = 1 /2 . 5) On the unit circle, the x coordinate is the cosine of the angle, and the y coordinate is the sine of the angle: So x = - 1/2 and y = - ∛3/2. 6) You can check on a calculator; sin 240° = -0.866... and cos 240° = -0.5. The answer is therefore: A: - ∛3 / 2, for the y coordinate, and C: - 1/2 for the x coordinate.
Step by step explanation: Given: The measure of the angle θ is 600°. To find: The point (x, y) corresponding to θ on the unit circle is ? Solution: We know that on the unit circle, the x and y coordinates are the cosine and sine ratios respectively. Now we have given θ = 600° 1 circle = 360° So 600° corresponds to 600° – 360° = 240°. i.e. θ = 360° + 240° 180° < 240° < 270° ⇒ the point is in the third quadrant i.e. the x and y coordinates are negative. Now the additional angle for using notable angles: 240° - 180° = 60° The sine and cosine of 60° are known: On the unit circle the abscissa is the cosine of the angle, and the ordinate is the sine of the angle. The coordinates are therefore.
Θ = 600° 1 circle = 360° Θ = 360° + 240° (x,y) = cos 360° , sin 240° (x,y) = -0.50 , -0.886 If these are the given options: A .) -(3^(1/2))/2 B.)-1(2^(1/2))/2 C.)-1/2 D.) (3^(1/2))/ 2 x = C) – 1/2a = A) -(3^1/2) / 2
Answer 6
sinα=y/1 and cosα=x/1 then The point corresponding to the angle of 600° is: (cos600, sin600) i.e. approximately (-1/2, -√(3/4)