Question

If cos(Θ) = -2 9 , and 90° < θ < 180°, what is the value of tan(θ)?

A) -77sqroot/2

b) -77sqroot/9

c) 77sqroot/2

d) 77sqroot/9

e) 65sqroot/9

Answer 1

we know that

if 90° < θ < 180°
then
θ--------------> belong to the second quadrant
so
tan θ is negative

sin² θ + cos² θ=1----------> sin² θ=1-cos² θ----->sin² θ=1-(-2/9)²
sin² θ=1-(4/81)------> 77/81----------> sin θ=√(77/81)------> √77/9
sin θ=(√77)/9

tan θ=sin θ/cos θ------> [(√77)/9]/[-2/9]-------> -√77/2

the answer is the option
A) -77sqroot/2