Question

EXERCISES 4 (a)state which of the following are positive and how?(i) cos 271(ii) sec 73°(iv) cosec 159°sec 199°(vi) cos 315º (viii) Co 375°(ii) sin 302(vi) cosec 126LC.trigonometric ralios of some acute⁸​

Answer 1

Given : (i) cos 271(ii) sec 73°(iv) cosec 159°sec 199°(vi) cos 315º (viii) Co 375°(ii) sin 302(vi) cosec 126

To Find : state which of the following are positive  

Solution:

Sin/Cosec    0°  to 180°    + ve       180°  to  360°   - ve

Cos/Sec    0° to 90°  and 270° to 360° + ve    and   90°  to 270°  - ve

cos 271°    between  270° and  360°   hence  +ve

sec 73°       between  0° and  90°   hence  +ve

cosec 159°      between  0°  to 180°  hence  +ve

sec 199°    between  90°  to 270°  hence  -ve

cos 315º    between 270° to 360°  hence  +ve

Cos 375° = Cos 15°  between  0° to 90°  hence  +ve

sin 302°   between 180° to 360°  hence  -ve

cosec 126° between  0°  to 180°  hence  +ve  

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Answer 2

$\sf { \underline{SOLUTION}}$

TO CHECK

Which of the following are positive

(i) cos 271°

(ii) sec 73°

(iii) cosec 159°

(iv) sec 199°

(v) cos 315º

(vi) cos 375°

(vii) sin 302°

(vii) cosec 126°

CONCEPT TO BE IMPLEMENTED

i) In the first quadrant ( 0° < θ < 90° ) all trigonometric ratios are positive

ii) In the second quadrant ( 90° < θ < 180° ) sin , cosec are positive and all other trigonometric ratios are positive

iii) In the third quadrant ( 180° < θ < 270° ) tan , cot are positive and all other trigonometric ratios are positive

iv) In the second quadrant ( 270° < θ < 360° ) cos , secare positive and all other trigonometric ratios are positive

EVALUATION

CHECKING FOR cos 271°

Here the angle is 271°

The angle lies in Fourth Quadrant

Hence cos 271° is positive

CHECKING FOR sec 73°

Here the angle is 73°

The angle lies in First Quadrant

Hence sec 73° is positive

CHECKING FOR cosec 159°

Here the angle is 159°

The angle lies in second Quadrant

Hence cosec 159° is positive

CHECKING FOR sec 199°

Here the angle is 199°

The angle lies in third Quadrant

Hence sec 199° is negative

CHECKING FOR cos 315°

Here the angle is 315°

The angle lies in Fourth Quadrant

Hence cos 315° is positive

CHECKING FOR cos 375°

Here the angle is 375°

375° = ( 4 × 90° ) + 15°

The angle lies in First Quadrant

Hence cos 375° is positive

CHECKING FOR sin 302°

Here the angle is 302°

The angle lies in Fourth Quadrant

Hence sin 302° is negative

CHECKING FOR cosec 126°

Here the angle is 126°

The angle lies in second Quadrant

Hence cosec 126° is positive

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