# Find one positive angle and one negative angle that are coterminal with 255 degrees

###### Question:

## Answers

10) 615° & -105°

12) -440° & 280°

Step-by-step explanation:

Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.

Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.

10) 255° + 360° = 615° (this is a POSITIVE coterminal angle to 255°)

255° - 360° = -105° (this is a Negative coterminal angle to 255°)

12) -800° + 360° = -440° (this is a Negative coterminal angle to -800°)

-440° + 360° = -80° (this is a Negative coterminal angle to -800°)

-80° + 360° = 280° (this is a POSITIVE coterminal angle to -800°)

13π/4 , 21π/4, -3π/4, -11π/4

Step-by-step explanation:

Coterminal Angles are angles which share the same initial side and terminal sides.

To find coterminal angles, simply add or subtract 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

5π/4 =(4π/4)+(π/4)

Our Angle 5π/4 is in the 3rd quadrant and exceeds π radians by (π/4) radians, or 45° angular measure.

The 2 positive co-terminal angles would be:

Adding 2π

5π/4 + 2π = 13π/4

Adding another 2π

5π/4 + 2π +2π = 21π/4

The two negative co-terminal angles would be:

Subtracting 2π

5π/4 - 2π = -3π/4

Subtracting another 2π

5π/4 - 2π -2π = -11π/4

The coterminal angles are:

13π/4 , 21π/4, -3π/4, -11π/4

Step-by-step explanation:

positive angle =300+180=480.

negative angle = 300 -180=120

The answer is below

Step-by-step explanation:

Let us assume the angle is -π/4.

Coterminal angles are angles that have the same initial side and terminal side. They are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.

Positive coterminal angles are gotten by adding 360° if the angle is in degrees or 2π for angles in radian while negative coterminal angles are gotten by subtracting 360° if the angle is in degrees or 2π for angles in radian.

Positive coterminal angle = -π/4 + 2π = 7π/4, 7π/4 + 2π = 15π/4

Positive coterminal angle = 7π/4, 15π/4

Negative coterminal angle = -π/4 - 2π = -9π/4, -9π/4 - 2π = -17π/4

Negative coterminal angle = -9π/4, -17π/4

The correct answer is 450°, 810°, -270° and -630°.

Step-by-step explanation:

According to the given scenario, the calculation of the two positive angles and two negative angles i.e. coterminal is as follows:

The coterminal angles are the angles in which the difference could be 360 degrees or the multiples of 360 degrees

For 90 degrees, the two positive angles are

a. 90° + 360°

= 450°

450° + 360°

= 810°

b. The two negative angles are

= 90° - 360°

= -270°

-270° - 360°

= -630°

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians .

Notice the picture below

negative angles, are just angles that go "clockwise", namely, the same direction a clock hands move hmmm so.... and one revolution is just 2π

now, you can have angles bigger than 2π of course, by simply keep going around, so, if you go around 3 times on the circle, say "counter-clockwise", or from right-to-left, counter as a clock goes, 3 times or 3 revolutions will give you an angle of 6π, because 2π+2π+2π is 6π

now... say... you have this angle here... let us find another that lands on that same spot

by simply just add 2π to it :)

[tex]\bf \cfrac{7}{6}+2=\cfrac{19}{6}\qquad thus\qquad \cfrac{7\pi} {6}+2\pi =\cfrac{19\pi }{6} \\\\\\ \cfrac{19\pi }{6}\impliedby co-terminal\ angle[/tex]

now, that's a positive one

and [tex]\bf \cfrac{7}{6}-2=-\cfrac{5}{6}\qquad thus\qquad \cfrac{7\pi} {6}-2\pi =-\cfrac{5\pi }{6} \\\\\\ -\cfrac{5\pi }{6}\impliedby \textit{is also a co-terminal angle}[/tex]

to get more, just keep on subtracting or adding 2π

[tex]The measure of an angle in standard position is given. find two positive angles and two negative ang[/tex]

Subtracting or adding multiples of 2*r to any angle will make no change, it will be the same angle.

7*pi/6 = 6*pi/6 + pi/6

So, the angle is in the third quadrant and surpasses pi radians by pi/6 radians or 30 degrees.

The positive co-terminal angles are:

Adding 2*pi,

7*pi/6 + 12*pi/6 = 19*pi/6

Adding another 2*pi,

7*pi/6 + 2*(12*pi)/6 = 7*pi/6 + 24*pi/6

7*pi/6 + 24*pi/6 = 31*pi/6

The 2 negative co-terminal angles are:7*pi/6 – 12*pi/6 = 5*pi/6

And

7*pi/6 – 24*pi/6 = -17*pi/6

You can add and subtract suitable multiples of 2π to find your co-terminal angles.

5π/4 + 2π = 13π/4

5π/4 + 2·2π = 21π/4

5π/4 - 2π = -3π/4

5π/4 - 2·2π = -11π/4

Your angles can be {-11π/4, -3π/4, 13π/4, 21π/4}.

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