Answer:
(I)Sin Θ=4/5
(II) Cos Θ =-3/5
(III) Tan Θ = -4/3
(IV) Cosec Θ = 5/4
(V) Sec Θ = -5/3
(VI) Cot Θ = -3/4
Step-by-step explanation:
(-24,18)
This lies in the second quadrant from the diagram.
Note that the angle is at the origin (0,0).
Using Pythagoras triples(18,24,30)
Hypotenuse = 30
Opposite=-24
Adjacent=18
(I)Sin Θ= Opposite/Hypotenuse
=-24/30=-4/5
Note: (Sine is Positive in the Second Quadrant)
Sin Θ =4/5
(II) Cos Θ = Adjacent/Hypotenuse
=18/30=3/5
Since Cosine is negative in the Second Quadrant
Cos Θ=-3/5
(III) Tan Θ = Opposite/Adjacent
Tan Θ = -24/18= -4/3
(IV) Cosec Θ = 1/Sin Θ = 5/4
(V) Sec Θ = 1/cos Θ = -5/4
(VI) Cot Θ = 1/tan Θ = -3/4
