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Ket [755]
3 years ago
6

Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values

of the remaining five trigonometric functions of theta
Mathematics
1 answer:
diamong [38]3 years ago
3 0

The exact values of the remaining <u>five</u> trigonometric functions of theta are

  • sinθ = √3/2
  • cosecθ = 2/√3
  • cosθ = -1/2
  • secθ = -2
  • cotθ = -1/√3

Since tanθ = -√3.

The remaining <u>five</u> 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 <u>five</u> 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:

brainly.com/question/4515552

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