Answer:
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
