 Krishna
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Step 1:  Know about the unit circle

NOTE: Any point on the unit circle will be a distance of one unit from the center

this is the definition of the unit circle.

•   The terminal side of an angle \theta in standard position intersects the unit circle at  (\cos \theta, \sin \theta).
•   Another thing you can see from the unit circle is that the values of sine and cosine will never be more than 1 or less than –1.

Step 2: Confirm that the point they have given is a point on the unit circle or not

NOTE: To confirm, apply the Pythagoras theorem to find the length of the radius of the right triangle formed by dropping a perpendicular from the x-axis down to the point.

Pythagoras theorem: hypotenuse^2 = side^2 + side^2 EXAMPLE: Given sides x = \frac{77}{85}, y = \frac{36}{85}

The Pythagorean Theorem given a value for the radius = 1,

So, I confirmed that the point is on the unit circle.

Step 2: Find the trigonometric ratio values by using the unit circle

NOTE: The terminal side of an angle \theta in standard position intersects the

unit circle at  (\cos \theta, \sin \theta).

The given point (\frac{77}{85}, \frac{36}{85})

Therefore,   \cos \theta = \frac{77}{85}  , \sin \theta = \frac{36}{85}