If cosΘ= -4/5, and Θ is a third quadrant angle, find the value of sinΘ and cscΘ, Please explain the steps in

Question

simple terms please so that I can catch on.

Answer 1

You know that sin^2 + cos^2 = 1. So if cos = -4/5 then sin^2 = 1 - 16/25 = 9/25. Take the square root to get sin = +/- 3/5.

But there are two places on the circle at which sin = + 3/5. One is in quadrant I and the other in quadrant II. There are also two places where sin = -3/5, namely in quadrants III and IV. But in quadrant IV, the cosine is positive, so the solution is that sin = -3/5 in quadrant III.

csc is just 1/sin, so in this case csc = -5/3.

Answer 2

At the third quadrant, the sin is negative, cos is negative, and the tangent is positive.
If you are able to recall a 3, 4, 5 triangle, it mostly means you are able to do it.
cos@=-4/5
One of the sides must be 4, so the other side is -3
sin@=-3/5
Tangent=3/4
Just imagine the sides.

Answer 3

draw a triangle to solve problem

x^2 = 5^2 - 4^2
x^2 = 25-16
x^2 = 9
x = 3

hypotenuse = 5
side = 4
opposite =3

cosΘ= -4/5

sin Θ = -(opposite / hypotenuse)
sin Θ = -(3/5)
sin Θ = -3/5#

csc Θ = 1/ sin Θ
csc Θ = 1/(-3/5)
csc Θ = -5/3#

Answer 4

locate cos by doing (-a million/4)^2+cos^2=a million. You get sq. root of 15 over 4. next yet another identity for sin2x is 2sinxcosx. So multiply your values for sin and cos by both. 2(-a million/4 x -sq. 15/4). you eventually end up with -sq. of 15/8. EDIT:: i didnt propose neg. sorry, yet i answered first and its good so i might want to get the criteria =]

Answer 5

Vertical side = - 3
sin Ө = - 3/5 (sin is -ve in 3rd quadrant)
cosec Ө = 1 / sinӨ = 1 / (- 3/5) = (- 5/3)