Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = -17/18. Find the exact values of the five remaining trigonometric functions of θ. Find the exact values of the five remaining trigonometric functions of θ.

These are the five remaining trigonometric functions:

tanθ = -18/17

cosθ = 17(√613) / 613

secθ = (√613) / 17

sinθ = - 18(√613) / 613

cscθ = - (√613)/18

Step-by-step 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

your answer would be 12

answer is 33

step-by-step explanation: