so you already know what cos is. csc is 1/sin. so its 1/(-root3/2) which is -2root3/3
cot is cos/sin so that's root3/2
just for future references, you might want to check if your school/public library has tutor.com where you can get a tutor for almost anything. they also have videos of how to solve problems. you could also try those trig calculators on line where they show you what they did. and you should always be able to find answers to these types of trig problems right there on the unit circle.
Comments
4/3 pi is > pi =180o so the angle is in the bottom right where adjacent and opposite are negative.
The angle is pi/3 or 60o beyond 180o. Here both the opposite and adjacent sides are -ve
cos theta =a/h = -1/2
csc theta = 1/sin = h/o = -2/SQRT(3) = -2 SQRT(3)/3
cot theta = 1 /tan = a/o =1/SQRT(3) = SQRT(3)/3
4pi/3 on the unit circle is (-1/2, -root3/2)
the coordinates are (cos, sine)
so you already know what cos is. csc is 1/sin. so its 1/(-root3/2) which is -2root3/3
cot is cos/sin so that's root3/2
just for future references, you might want to check if your school/public library has tutor.com where you can get a tutor for almost anything. they also have videos of how to solve problems. you could also try those trig calculators on line where they show you what they did. and you should always be able to find answers to these types of trig problems right there on the unit circle.
cos = -1/2
csc = -2/sqrt 3
cot = 1/sqrt3
i do it by memorizing the unit circle:
cos(4pi/3) = -1/2
csc(4pi/3) = 1 / sin(4pi/3)
= 1 / -sqrt(3) / 2
= -2sqrt(3) / 3
cot(4pi/3) = 1 / tan(4pi / 3)
= cos(4pi/3) / sin(4pi/3)
= (-1/2) / (-2sqrt(3) / 3)
= 3 / 4sqrt(3)
= sqrt(3) / 4
Sol cos(4(pi)/3) = cos(240 degrees)
= cos (180+60)
= - cos(60)
= -(1/2)
cos(4(pi)/3)= -1/2 ..................Ans
cscθ = 1/(sinθ) ................(i)
(sinθ) =sin(4(pi)/3)
= sin(240)
= sin(180+60)
= -sin 60
= -{sqrt(3)/2}
Therefore cosec(θ) = -2/(sqrt(3)) .....................Ans
cotθ= cosθ / sinθ = {-1/2}/{-sqrt(3)/2} = 1/sqrt(3) ................Ans
Θ = 4π/3 = π + π/3
cosΘ = cos(π+π/3) = cos(π)cos(π/3) - sin(π)sin(π/3)
cos(π) = -1
sin(π) = 0
cosΘ = -cos(π/3) = -1/2
cscΘ = 1/sinΘ
sinΘ = sin(π)cos(π/3) + cos(π)sin(π/3) = -sin(π/3) = -√3/2
cscΘ = 1/(-√3/2) = -2/√3 = -2√3/3
cotΘ = cosΘ/sinΘ = (-1/2)/(-√3/2) = 1/√3 = √3/3
cosθ = -1/2
cscθ = [(square root of)3]/2
cotθ = -1/[(square root of)3] = -[(square root of)3]/3