How do you find the sine, cosine, and tangent of 4pie/3?

Question

it says t = 4 pie over 3 and find the sine cosine and tangent of it

Answer 1

4π/3 is in quadrant III with a reference angle of 60 degrees. Memorize

1, √3, 2 as the sides of a 60 degree right triangle, the sides are in the order x, y , r

in quadrant III both x and y are negative, so the ratios that apply are

x,y, r = -1, -√3, 2

sin 4π/3 = -√3/2

cos 4π/3 = -1/2

etc. I will let you finish the problem.

Answer 2

ok First find what this angle is on the unit circle.

4pi/3 is pi/3 radians past pi. so the refrence angle is pi/3 and is in the Quadrant III(the refrence angle is the angle from the x-axis).

Sine is negative in quadrant 3. so take the -sin(pi/3). that equals (-1)(sin(pi/3))=(-1)(sqrt3/2)=(-sqrt3)/2

cosine is also negative in quad 3 so we have -cos(pi/3)=

(-1)(cos(pi/3))=(-1)(1/2)=

-1/2

tangent is easy if you know that sinx/cosx=tanx

so sin(4pi/3)/cos(4pi/3)=tan(4pi/3)

((-sqrt3)/2)/(-1/2)

sqrt3

sin(4pi/3)=(-sqrt3)/2

cos(4pi/3)=-1/2

tan(4pi/3)=sqrt3

Answer 3

4pie/3 = 240 degrees

sin 240 = - sqrt 3/2

cos 240 = -1/2

tan 240 = sqrt 3