Question

state whether the following trigonometric values are positive or negative a)sec(-120⁰) d) cosec(13pi/12) e) cos(-7pi/6) f) cot(1420⁰)​

Answer 1

SOLUTION

TO DETERMINE

To state which of the following trigonometric values are positive or negative

a)sec(-120°)

b) cosec(13π/12)

c) cos(-7π/6)

d) cot(1420°)

EVALUATION

a) sec(-120°)

= sec 120°

Since the angle 120° lies in second quadrant

So sec 120° is negative

Hence sec(-120°) is negative

b) cosec(13π/12)

= cosec 195°

Since the angle 195° lies in second quadrant

So cosec 195° is positive

Hence cosec(13π/12) is positive

c) cos(-7π/6)

= cos 7π/6

= cos 210°

Since the angle 210° lies in second quadrant

So cos 210° is negative

Hence cos(-7π/6) is negative

d) cot(1420°)

Since the angle 1420° lies in fourth quadrant

So cot 1420° is negative

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Answer 2

Answer ⤵️

To Find ⤵️

To state which of the following trigonometric values are positive or negative.

a)sec(-120°)

b) cosec(13π/12)

c) cos(-7π/6)

d) cot(1420°)

Calculation ⤵️

a) sec(-120°)

= sec 120°

Since the angle 120° lies in second quadrant.

This means that sec 120° is negative.

Therefore sec(-120°) is negative.

b) cosec(13π/12)

= cosec 195°

Since the angle 195° lies in second quadrant.

This means that cosec 195° is positive.

Therefore cosec(13π/12) is positive.

c) cos(-7π/6)

= cos 7π/6

= cos 210°

Since the angle 210° lies in second quadrant.

This means that cos 210° is negative.

Therefore cos(-7π/6) is negative.

d) cot(1420°)

Since the angle 1420° lies in fourth quadrant.

Therefore cot 1420° is negative.

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