The exact values of the remaining five trigonometric functions of theta are
- sinθ = √3/2
- cosecθ = 2/√3
- cosθ = -1/2
- secθ = -2
- cotθ = -1/√3
Since tanθ = -√3.
The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.
The next trigonometric function of θ is cotθ.
cotθ = 1/tanθ
= 1/-√3
= -1/√3.
Also, tan²θ + 1 = sec²θ
Substituting tanθ = -√3 into the equation, we have
(-√3)² + 1 = sec²θ
3 + 1 = sec²θ
sec²θ = 4
secθ = ±√4
secθ = ±2
Since θ is in the quadrant II,
secθ = -2
Also, cosθ = 1/secθ
= 1/-2
= -1/2
Also, cot²θ + 1 = cosec²θ
Substituting cotθ = -1/√3 into the equation, we have
(-1/√3)² + 1 = cosec²θ
1/3 + 1 = cosec²θ
cosec²θ = 4/3
cosecθ = ±√(4/3)
cosecθ = ±2/√3
Since θ is in the quadrant II,
cosecθ = +2/√3
Also, sinθ = 1/cosecθ
= 1/2/√3
= √3/2
So, the exact values of the remaining five trigonometric functions of theta are
- sinθ = √3/2
- cosecθ = 2/√3
- cosθ = -1/2
- secθ = -2
- cotθ = -1/√3.
Learn more about trigonometric functions here:
https://brainly.com/question/4515552
