Angles in standard position are always shown on the Cartesian plane. The x-axis and the y-axis divide the plane into four quadrants
On a Cartesian plane, you can generate an angle by rotating a ray about the origin.
The starting position of the ray, along the positive x-axis, is the initial arm of the angle. The final position, after a rotation about the origin, is the terminal arm of the angle.
An angle is said to be an angle in standard position if its vertex is at the origin of a coordinate grid and its initial arm coincides with the positive x-axis.
Draw the angle with the given measure in standard position.
Problem 1 :
−340°
Solution :
-340°
Moving clockwise rotation, should land at 1^{st} quadrant.
Problem 2 :
150°
Solution :
150°
Moving clockwise rotation, should land at 2^{nd} quadrant.
Problem 3 :
-185°
Solution :
-185°
Since the given angle is negative, we move in clock wise direction. The terminal side will lie on the 2^{nd} quadrant.
Problem 4 :
300°
Solution :
300°
Since the given angle is positive, we move in counter clock wise direction. The terminal side will lie on the 4^{th} quadrant.
Problem 5 :
-260°
Solution :
-260°
Since the given angle is negative, we move in clock wise direction. The terminal side will lie on the 2^{nd} quadrant.
Problem 6 :
220°
Solution :
220°
Since the given angle is positive, we move in counter clock wise direction. The terminal side will lie on the 3^{rd} quadrant.
Find the measure of each principal angle.
Problem 7 :
Solution :
Direction of rotation = clock wise rotation.
Angle should be negative and its terminal side is on the first quadrant.
- 270 - 20 = -290°
So, the required angle is -290°.
Problem 8 :
Solution :
Direction of rotation = counter clock wise rotation.
Angle should be positive and its terminal side is on the second quadrant.
90 + 30 = 120°
So, the required angle is 120°.
Problem 9 :
Solution :
Direction of rotation = counter clock wise rotation.
Angle should be positive and its terminal side is on the first quadrant.
90 - 30 = 60°
So, the required angle is 60°.
Problem 10 :
Solution :
Direction of rotation = clock wise rotation.
Angle should be negative and its terminal side is on the first quadrant.
= -270 - (90 - 80)
= -270° - 90 + 80
= -280°
So, the required angle is -280°.
Problem 11 :
Solution :
Direction of rotation = clock wise rotation.
Angle should be positive and its terminal side is on the third quadrant.
180 + 180 - 160 = 200°
So, the required angle is 200°.
Problem 12 :
Solution :
Direction of rotation = counter clock wise rotation.
Angle should be positive and its terminal side is on the first quadrant.
270 + 90 - 80 = 280°
So, the required angle is 280°.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM