Coterminal angles are the ones angles that proportion the equal initial and terminal facets. Their angles are drawn inside the preferred function in a manner that their initial sides will be at the positive x-axis and they may have the identical terminal facet like one hundred ten° and -250°.
In keeping with the coterminal definition:
You can find any fine and negative coterminal angle by adding and subtracting a few revolutions. For instance, if the selected attitude is α = 14°, you might find coterminal angles as follows by adding and subtracting 10 revolutions:
To locate coterminal angles in steps comply with the subsequent process:
Example 1:
Determine the coterminal angle of \( \frac{3\pi}{2} \)
Solution:
Given Angle: \( \theta = \frac{3\pi}{2} \),
Which is in radians,
Therefore, to calculate its coterminal angles, multiples of (2pi) are added to or subtracted from it.
Now, subtract \( 2\pi \) from the angle:
$$ \frac{3\pi}{2} - 2\pi $$
$$ = \frac{3\pi}{2} - \frac{4\pi}{2} $$
$$ = \frac{-\pi}{2} $$
Hence, the coterminal angle of \( \frac{3\pi}{2} \) is equal to \( \frac{-\pi}{2} \).
A Coterminal Angle Lens is an instrument that helps in identifying angles that align on the identical terminal plane when graphed within a coordinate frame. Angles change by several times 360 degrees (or twice π radians) but lead in the identical way.
Terminal angles occur when integrating or subtracting units of 360° (or two times π) radians. For example, terminal angles of 45° are 405° (45° plus 360°) and -315° (45° minus 360°).
Coterminal angles are critical in trigonometry because their corresponding sin, cos, and tan measurements are identical. This makes them useful in simplifying calculations and solving equations.
In this situation, a negative thirty degrees (°) carries a similarity or similarity with three hundred thirty degrees (°) since adding together three six zero degrees (°) and negative thirty degrees (°) gives us three hundred thirty degrees (°).
To find a positive angle that is similar, add 360° or 2π until you land positive. A pleasant congruent angle of minus forty-five degrees is three hundred fifteen degrees (minus forty-five degrees plus three hundred sixty degrees).
Locate a negative Coterminal angle by deducing 360° (or 2π radians) from the supplied angle. A counter-directional angle of 60° is -300° (60° - 360°).
Yes, angles in radians also have coterminal angles. You can find them by adding or subtracting 2π. Examples of coterminal angles are 9π/4 (π/4 + 2π) and -7π/4 (π/4 - 2π).
There are countless angles that are similar because you can continually add or deduct a full circle (360 degrees or 2π radians) endlessly.
This computer device is advantageous in the disciplines.
The Angle Companion is equipped to calculate angles in both degrees and radians, allowing users to calculate coterminal angles efficiently in either measurement system.
