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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.

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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

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