Answer:
These are the five remaining trigonometric functions:
tanθ = -18/17
cosθ = 17(√613) / 613
secθ = (√613) / 17
sinθ = - 18(√613) / 613
cscθ = - (√613)/18
Explanation:
The fourth quadrant corresponds to the angle θ in the interval 270°<θ<360°.
In this quadrant:
sine is negative
cosine is positive
tangent is negative.
Recall that cotangent is the inverse of tangent. Therefore:
cot θ= Adjacent/Opposite
If cotθ = -17/18.
Adjacent=-17
Opposite= 18
Using Pythagoras Theorem
Hypotenuse ² = (-18)²+17² =613
Hypotenuse =√613
The three sides of the right triangle are therefore:
Hypotenuse =√613
Adjacent=-17
Opposite= 18
(I)Tan θ= Opposite/Adjacent
Tan θ = -18/17.
(II)cos θ = Adjacent/Hypotenuse
= 17/√613= 17(√613) / 613
(III)sec θ is the inverse of cos θ
secθ =Hypotenuse/Adjacent
= (√613) / 17
(IV)sin θ = Opposite/Hypotenuse= -18/√613= - 18(√613) / 613
(V)Cosec θ is the inverse of Sine θ cscθ = Hypotenuse/Opposite=
- (√613)/18