Question

Which of the following expressions have a value of –√3?

sin(11π/6)
cos(5π/3)
cot(7π/6)
tan(11π/6)
cot(2π/3)
sin(5π/3)
csc(5π/3)
cos(7π/6)
cos(π/6)
csc(2π/3)

it's in Quadrant 4.
Trig table and unit circle give -->
2π/3+π=5π/3
Is it sin 5pi/3?


thank you

Answer 1

clearly not sin or cos, since √3 > 1
you know that tan π/3 = cot π/6 = √3
since you have -√3, the angle will be in QII or QIV
That gives you
tan(2π/3) = tan(5π/3) = -√3
cot(5π/6) = cot(11π/6) = -√3

Since none of those is listed, I suspect a typo. If you had -1/√3 then you get
cot(2π/3) = cot(5π/3) = -1/√3
tan(5π/6) = tan(11π/6) = -1/√3