Determine the quadrant in which each angle lies. (The angle measure is given in radians.)
1. (5π/6)
a) first quadrant
b) second quadrant
c) third quadrant
d) fourth quadrant
i think it is a)
2. -(5π/3)
a) first quadrant
b) second quadrant
c) third quadrant
d) fourth quadrant
i think it is b)
Trash Bad not good at all do stuff better so we can under stand
Oh, I see what you did there! But unfortunately, your answers are a bit off. Let me clown around with this and give you the correct responses:
1. (5π/6) - This angle falls in the second quadrant, so the correct answer is b) second quadrant.
2. -(5π/3) - This angle is in the third quadrant, so the right answer is c) third quadrant.
Keep up the good work, but don't clown around too much with those quadrants!
1. (5π/6) lies in the second quadrant.
To determine the quadrant in which an angle lies, we look at the sign and magnitude of the given angle measure. Since (5π/6) is positive and greater than π/2, it falls in the second quadrant.
Therefore, the correct answer is b) second quadrant.
2. -(5π/3) lies in the third quadrant.
Again, we look at the sign and magnitude of the given angle measure. Since -(5π/3) is negative and greater than π/2, it falls in the third quadrant.
Therefore, the correct answer is c) third quadrant.
To determine the quadrant in which each angle lies, we can use the following guidelines:
1. For an angle that is in the first quadrant, both the x-coordinate and the y-coordinate of the point on the unit circle are positive.
2. For an angle that is in the second quadrant, the x-coordinate is negative and the y-coordinate is positive.
3. For an angle that is in the third quadrant, both the x-coordinate and the y-coordinate are negative.
4. For an angle that is in the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative.
Now let's apply these guidelines to the given angles:
1. (5π/6):
To determine the quadrant in which this angle lies, we need to locate the point (cos(5π/6), sin(5π/6)) on the unit circle.
By evaluating cos(5π/6) and sin(5π/6), we get:
cos(5π/6) = -1/2 (negative)
sin(5π/6) = √3/2 (positive)
Since the x-coordinate is negative and the y-coordinate is positive, we can conclude that the angle (5π/6) lies in the second quadrant.
So, the correct answer is b) second quadrant.
2. -(5π/3):
Similarly, to determine the quadrant in which this angle lies, we need to locate the point (cos(-(5π/3)), sin(-(5π/3))) on the unit circle.
By evaluating cos(-(5π/3)) and sin(-(5π/3)), we get:
cos(-(5π/3)) = -1/2 (negative)
sin(-(5π/3)) = -√3/2 (negative)
Since both the x-coordinate and the y-coordinate are negative, we can conclude that the angle -(5π/3) lies in the third quadrant.
So, the correct answer is c) third quadrant.
1. 5pi/6 = 5*180/6 = 150o. 2nd Quad.
2. -(5pi/3) = -(5*180/3) = -300o. 1st quad.
The negative sign means 300o CW rotation from due East; That places the
vector in the 1st quadrant and is equivalent to 60o CCW.