Answer:
(a) Choice A + everywhere in (π/2, 3π/4)
(b) Choice A - everywhere in (π/2, 3π/4)
(c) Choice A - everywhere in (π/2, 3π/4)
Explanation:
This can be answered by knowing that the interval (π/2, 3π/4) lies in the second quadrant which lies between π/2 and π
π/2 = 90° and 3π/4 = 135° which lies in the second quadrant
If an angle θ lies in the first quadrant, we have the following facts:
sin(θ) is positive
cos(θ) is negative
tan(θ) = sin(θ)/cos(θ) is also negative (+ve divided by -ve is negative)
Therefore sin(t) is positive in the interval (π/2, 3π/4).
Correct choice is A
(b)
cos(t) is negative in the interval (π/2, 3π/4).
Choice A
(c) tan(t) is negative in the interval (π/2, 3π/4).
Choice A
At t = π/2 tan(t) is undefined