if cscθ =8/3 , then csc(-θ ) =

Question

if cscθ =⁸/3 , then csc(-θ ) =

Answer 1

csc(θ) = 8/3 there csc(-θ) = -8/3 because cosecant is an odd function. Note that sine, tangent, cosecant, and cotangent are odd; Cosine and secant are even.

Answer 2

csc(theta)= 8/3

sin(theta) =3/8 = .375

theta is in quadrant I or II

theta = 22.02 degrees or 180-22.02 = 157.98 degrees

-theta = -22.02 or - 157.98 degrees

csc(-theta) = csc(-22.02) = -8/3

or csc(-theta) = csc(-157.98) = -8/3

csc(-theta) =--csc(theta) 8/3 = -(-8/3)