Determine two coterminal angles (one positive and one negative) for the given angle. Give your answers in radians.
a) 8pie/9 b)8pie/45
I know that you have to add 2pie but I do not know how to do that.
Coterminal angles for an angle α are angles of the form α±2kπ where k is different from zero.
For example, some coterminal angles of π/2 are:
π/2 - 4π = -(7/2)π
π/2 - 2π = -(3/2)π
π/2 + 2π = (3/2)π
π/2 + 4π = (7/2)π
The last two should read:
π/2 + 2π = (5/2)π
π/2 + 4π = (9/2)π
To find coterminal angles, you can add or subtract multiples of 2π (or 360°) to the given angle. Here's how you can do it:
a) For the angle 8π/9:
To find the positive coterminal angle, add 2π:
8π/9 + 2π = (16π + 18π) / 9 = 34π/9
To find the negative coterminal angle, subtract 2π:
8π/9 - 2π = (8π - 18π) / 9 = -10π/9
So, the two coterminal angles for 8π/9 are 34π/9 and -10π/9.
b) For the angle 8π/45:
To find the positive coterminal angle, add 2π:
8π/45 + 2π = (8π + 90π) / 45 = 98π/45
To find the negative coterminal angle, subtract 2π:
8π/45 - 2π = (8π - 90π) / 45 = -82π/45
So, the two coterminal angles for 8π/45 are 98π/45 and -82π/45.
To find coterminal angles, you need to add or subtract a multiple of the full revolution, which is 2π radians or 360 degrees, to the given angle.
a) Given angle: 8π/9 radians
To find the positive coterminal angle, you can add 2π radians:
Positive coterminal angle: 8π/9 + 2π = 26π/9 radians
To find the negative coterminal angle, you can subtract 2π radians:
Negative coterminal angle: 8π/9 - 2π = -10π/9 radians
b) Given angle: 8π/45 radians
To find the positive coterminal angle, add 2π radians:
Positive coterminal angle: 8π/45 + 2π = 98π/45 radians
To find the negative coterminal angle, subtract 2π radians:
Negative coterminal angle: 8π/45 - 2π = -62π/45 radians
So, the positive coterminal angles are 26π/9 radians (a) and 98π/45 radians (b), while the negative coterminal angles are -10π/9 radians (a) and -62π/45 radians (b).