Question

A point on the terminal side of an angle theta in standard position is (negative 24 comma 18 ). Find the exact value of each of the six trigonometric functions of theta.

Answer 1

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