Answer:
3pi/ 10
Step-by-step explanation:
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Find the Reference Angle (17pi)/10
17π1017π10
Since the angle 17π/ 10 is in the fourth quadrant, subtract 17π/10 from2π.
2π−17π/10
The angle between 0 to [tex]2\pi[/tex] that is coterminal with [tex]-\frac{17\pi }{10}[/tex] is [tex]\frac{3\pi }{10}[/tex].
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.
Angles are considered to be in standard position if the initial side is on the positive x-axis and the vertex at the (0,0) point of the Cartesian plane. All angles generated that share the same terminal side are coterminal angles. These are angles that have differences of multiples of 360n or n2pi where n is an integer.
A coterminal angle is found by simply adding or subtracting 360 and its multiples.
The coterminal angles of 20 degrees for example are 20 + 360 = 380 or 20 - 360 = -340. This may continue by adding or subtracting 360 each time.
To get coterminal angles, you simply have to add or subtract 2[tex]\pi[/tex].
According to this problem,
We are looking for a coterminal angle that is between 0 to 2[tex]\pi[/tex], so we will add [tex]2\pi \ to \ \frac{-17\pi }{10}[/tex].
= [tex]\frac{-17\pi }{10} +\frac{20\pi }{10}[/tex]
= [tex]\frac{-17\pi +20\pi }{10}[/tex]
= [tex]\frac{3\pi }{10}[/tex]
Hence,
The angle between 0 to [tex]2\pi[/tex] that is coterminal with [tex]-\frac{17\pi }{10}[/tex] is [tex]\frac{3\pi }{10}[/tex].
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