Pythagorean identity help?

Question

I don't quite understand what to do in this question...
1. Use the Pythagorean identity:
Given that cos x = 3/5 and 3pi/2< x < 2pi, find sin x and tan x

Answer 1

The pythagorean identity is (cos x)^2+(sin x)^2=1 (Which is true regardless of x) Since you have cos x=3/5, you can insert that into the identity. Which gives you (3/5)^2+(sin x)^2=1 -> (sin x)^2=1-9/25 -> (sin x)^2=16/25 -> sin x= +/- 4/5
This gives two possible values of x:
x1 = 0.93
x2 = -0.93
Only x1 satisfies 3pi/2< x < 2pi. This means that sin x = 4/5 in this case.
tan x = sin x / cos x = (4/5)/(3/5) = 4/3

Answer 2

First off, they tell you the angle is 3pi/2 < x < 2pi, which means the angle lies in the fourth quadrant, where sin < 0, cos > 0
and tan < 0

The first pythagorean identity says:

cos^2 (x) + sin^2 (x) = 1
(3/5)^2 + sin^2 (x) = 1
sin^2 (x) = 1 - (9/25)
sin^2 (x) = (16/25)
sin (x) = +/- 4/5
But since sin < 0 in the fourth quadrant, sin (x) = -4/5

tan(x) = sin (x) / cos (x)
= -(4/5) / (3/5)
=- (4/3)

Answer 3

3pi/2 < x < 2pi
means x is in the fourth cuadrant (lower right) where cos is (+); sin is (-) and tan is (-)
cosˆ2(x)+ sinˆ2(x) =1
(3/5)ˆ2 - 1 = sinˆ2(x) ... solve sin(x) = sqrt(9/25 - 1)

tan x = sin x / cos x; sin x = 5tan(x)/3 ....

Answer 4

I think the 3pi/2 radians rather than degrees.
Or it could mean that "this is the range of your variable: 4.71
You know how to do a cosine funtion on an angle expressed in degrees right?? Do the reverse (arc-cosine???) and find out what x is (in degrees). Then do a sin and tan function on x.

Answer 5

3pi/2 < x < 2pi
is the same as saying
270° < x < 360°
or in this case
(0,-y) to (x,0)

sin(x) = y/r
cos(x) = x/r
tan(x) = y/x

cos(x) = (3/5)

x^2 + y^2 = r^2
3^2 + y^2 = 5^2
9 + y^2 = 25
y^2 = 16
y = 4 or -4

Following 3pi/2 < x < 2pi

y = -4

sin(x) = y/r
sin(x) = -4/5

tan(x) = -4/3

ANS :
sin(x) = -4/5
tan(x) = -4/3

Answer 6

x lis between 3pi/2 & 2pi tht means x lie in 4th qudrant.
cosx=3/5=b/h
therefore b=3, h=5
now h^2=p^2+b^2
so 25=p^2+9
so p=4. now sinx is negative in 4th quad. so sinx= -4/5
also tan is negative so tanx= -4/3

Answer 7

3pi/2< x < 2pi means that sinx<0 and cos x> 0(1)
sin^2x+cos^2 x=1;
sin^2x=1-cos^2x
sin x=sqrt(1-cos^2x) or sin x=-sqrt(1-cos^2x)(2)
(1),(2): sin x =-sqrt(1-cos^2x)
sin x =- sqrt(1-9/25);
sin x = - 4/5
tan x = sinx/cosx
tan x =- 4/3