Help with Trig, please? Copy and complete each statement iwth the proper trigonometric functions:?

Question

1. cos x= ? (x-90) = ? (x-180) = ? (x-270)
2. tan x= ? (x-90) = ? (x-180) = ? (x-270)
3. cot x= ? (x-90) = ? (x-180) = ? (x-270)
4. sec x= ? (x-90) = ? (x-180) = ? (x-270)
5. csc x= ? (x-90) = ? (x-180) = ? (x-270)

Please help me, I don't understand those.

Answer 1

#1. cos x = cos x ; cos (x-90) = - sin x ; cos (x-180) = -cos x; cos (x-270)= sin x

#2. tan x = (sin x)/(cos x) ; tan(x-90) = (-cos x) / (-sin x) = cot x; tan (x-180) = (-sin x)/(-cos x) = tan x ; tan(x-270) = (cos x) / (sin x) = cot x

#3. cot x = (cos x)/(sin x) ; tan(x-90) = (-sin x) / (-cos x) = tan x; cot (x-180) = (-cos x)/(-sin x) = cot x ; cot(x-270) = (sin x) / (cos x) = tan x

#4. sec x= 1/(cos x) ; sec(x-90) = 1/(- sin x) = - csc x ; sec(x-180) = 1/(- cos x) = - sec x ; sec(x-270) = 1/(sin x) = csc x

#5. csc x= 1/(sin x) ; sec(x-90) = 1/(-cos x) = - sec x ; sec(x-180) = 1/(-sin x) = -csc x ; sec(x-270) = 1/(cos x) = sec x

Answer 2

The problem is flawed. Let's look at 1.

1. cos x= ? (x-90) = ? (x-180) = ? (x-270)

Let x = 60

cos x = cos 60 = 1/2
cos(60-90) = cos(-30) = (√3)/2
cos(60-180) = cos(-120) = -1/2
cos(60-270) = cos(-210) = -(√3)/2

None of the answers are correct.

Answer 3

1. cos x= -sin (x-90) = -cos (x-180) = sin (x-270)
2. tan x= -cotg (x-90) = tan (x-180) = -tan (x-270)
3. cot x= -tan (x-90) = cotg (x-180) = -cotg (x-270)