1. 4cosx = 2
cosx = 2/4 = 1/2
I know cos π/6 = 1/2 , so x = π/6
but the cosine is positive in quadrants I or IV
so x is also 2π- π/6 = 11π/6
#2
sec^2 = 4/3
1/cos^2 x = 4/3
cos^2 x = 3/4
cos x = ± √3/2
so x could in any of the 4 quadrants
you should know the angle whose cosine is √3/2
you will have 4 answers, let me know what you got.
solve each equation if 0 < x < 2pi. answer must be in radians
1. 4 cos x - 2 = 0
2. 3 sec^2 - 4 = 0
5 answers
1.
cos x = 1/2
x = 60 or x = -60 which is 300 in degrees
or
x = pi/3 or x = 2pi-pi/3 = 5 pi/3 in radians
cos x = 1/2
x = 60 or x = -60 which is 300 in degrees
or
x = pi/3 or x = 2pi-pi/3 = 5 pi/3 in radians
1. 4cos(x)-2=0
cos(x)=1/2
x=acos(x)=1/2 between 0 and 2π
or π/3 or 5π/3 because cosine is positive in the first and fourth quadrants.
2. 3sec²(x)-4=0
3sec²(x)=4
cos²(x)=3/4
cos(x)=±(√3)/2
for
cos(x)=+(√3)/2
x=π/6, 11π/6
cos(x)=-(√3)/2
x=5π/6, 7%pi;/6
Back substitute all solutions in original equations to check the answers.
cos(x)=1/2
x=acos(x)=1/2 between 0 and 2π
or π/3 or 5π/3 because cosine is positive in the first and fourth quadrants.
2. 3sec²(x)-4=0
3sec²(x)=4
cos²(x)=3/4
cos(x)=±(√3)/2
for
cos(x)=+(√3)/2
x=π/6, 11π/6
cos(x)=-(√3)/2
x=5π/6, 7%pi;/6
Back substitute all solutions in original equations to check the answers.
Oh my!
I know that cos π/3 = 1/2 and cos π/6 = √3/2
(What is the matter with me ? )
I know that cos π/3 = 1/2 and cos π/6 = √3/2
(What is the matter with me ? )
I guess we all started at the same time, and I am the slowest of us all! :)
0 answers