Find the other trigonometric functions if
i) If coso
--
3
and 180° < < 270°.
5
Answers
Step-by-step explanation:
↗Let theta = A
Given
cos A = -3/2 where A lies in 3rd quadrant according to the equation 180° <A<270°
So we have to find all other trignometric angles that are :
sinA , tan A , cot A , sec A and cosec A
1 ) As we know that sec A is the reciprocal of cos A , so
cos A = -3/2
Then reciprocal of cos A will be the value of sec A
sec A = - 2/3
As sec A is also -ve in 3rd quadrant .
2) As we know that
\sin(a) = \sqrt{1 - \cos( {a}^{2} ) }sin(a)=
1−cos(a
2
)
\sin(a) = \sqrt{1 - {( \frac{ - 3}{2} )}^{2} }sin(a)=
1−(
2
−3
)
2
\sin(a) = \sqrt{1 - \frac{9}{4} }sin(a)=
1−
4
9
\sin(a) = - \frac{ \sqrt{5} }{2}sin(a)=−
2
5
As sin A also functions -ve in 3rd quadrant .
3) As we know that cosec is reciprocal of sin , so
sin A =- √5/2
Then Cosec will be reciprocal of it .
Cosec A = -2√5
As Cosec also functions-ve in 3rd quadrant.
4) As we know that
tan A = sin A / cos A so
We have already found the values of sin A and cos A ,so putting these values here
\tan(a) = \frac{ - \frac{ \sqrt{5} }{2} }{ - \frac{3}{2} }tan(a)=
−
2
3
−
2
5
tan A = √5/3
tan functions +ve in 3rd quadrant.
5) We know that cot is the reciprocal of tan , so
tan A = √5/3 then
cotA = 3/√5
As cot functions positive in 3rd quadrant.
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