97.2k views
1 vote
If cot x = 2 / 3 and x is in quadrant 4, find:
sin(x / 2)

User Buford
by
8.2k points

2 Answers

6 votes
Cot = adjacent / opposite = 2/3 but it lies in the 4th quadrant so 2/-3
Sin = opposite / hypotenuse , you have it as x/2
So you have the hypotenuse and the opposite is -3 so -3/2
Sin(-3/2) = -sin (3/2)
Alternative form : -0.997495
User Bleeding Fingers
by
8.0k points
3 votes
cos x / sin x = 2 / 3
2 sin x = 3 cos x
sin x = 3 cos x / 2
sin² x + cos² x = 1
9 cos² x / 4 + cos² x = 1 / * 4
9 cos² x + 4 cos² x = 4
13 cos² x = 4
cos x = 2 / √13
sin ( x/2 ) = √ [( 1 - cos x )/ 2] = √ [( 1 - 2/√13 ) / 2] = √(√13 - 2 )/(2√13)
or sin ( x/2 ) ≈ 0.471858
User Loilo
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories