Suppose there is a coordinate (−1,√3) at the end of a terminal arm and ߠ represents the angle
in standard position. determine the exact values of sin ߠ ,cos ߠ ,and tan ߠ. ( show work: ))

The exact values of sin T = √3/2 , cos T = -1/2 , tan T = -√3

Step-by-step explanation:

* Lets explain how to solve the problem

- The coordinates (-1 , √3) lie at the end of a terminal arm of angle T

 in the standard position

∵ x coordinate is negative value

∵ y coordinate is positive

∴ The terminal side of angle T lies in the 2nd quadrant

∴ ∠ T lies in the 2nd quadrant

- In the 2nd quadrant cos T , tan T are negative values but sin T is

 positive value

- The terminal side is the hypotenuse of the right Δ whose

  x-coordinate and y-coordinate are its legs, where y is the

  opposite side to angle t and x is the adjacent side to angle T

- The length of the hypotenuse r = √(x² + y²)

# Remember tan T = opposite/adjacent

∵ tan T = y-coordinate/x-coordinate

∵ x = -1 and y = √3

∴ tan T = √3/-1

∴ tan T = -√3

∵ r = √(x² + y²)

∴ r = √[(-1)² + (√3)²] = √[1 + 3] = √4 = 2

# Remember sin T = opposite/hypotenuse

∵ sin T = y-coordinate/r

∴ sin T = √3/2

# Remember cos T = adjacent/hypotenuse

∵ cos T = x-coordinate/r

∴ cos T = -1/2

* The exact values of sin T = √3/2 , cos T = -1/2 , tan T = -√3