5 Which of the following points is in the unit circle? (1)
a. (-√2 / 2 , -√2 / 2)
b. (√2 / 3 , -√2 / 3)
c. (1 / 2 , 1 / 2)
d. (3 / 2 , 2 / 3)
Answers
Answer:
a. (-√2 / 2 , -√2 / 2)
Step-by-step explanation:
Concept= Circles
Given= Radius of circle and various points
To Find= Which point is on unit circle
Explanation=
A Unit circle is circle with radius 1 and diameter2.
The Centre of unit circle is the intersection of x-axis and y-axis at (0,0).
Points lying on the unit circle can be in any 4 quadrant.
Points are identified by the sine, cosine formula.
In a unit circle the radius is 1 so the line extending to circle (on its surface) are 1unit. Now to locate a point we make right angle triangle from that point to center of circle. Here, the perpendicular length(height) is 1unit, base length is 1unit so according to Pythagoras theorem the hypotenuse will be √2unit.
To locate point we use know , the point is (sinФ,cosФ)= (1/√2, 1/√2). the value will always be from (0,π)
Now this point can lie on any quadrant according to sign.
Checking options
a) (-√2 / 2 , -√2 / 2)
this can be reduced to (-1/√2, -1/√2), hence this point lies in 3rd quadrant and also on the unit circle.
Therefore (-√2 / 2 , -√2 / 2) lies in unit circle.
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