Easy Trig (1 Viewer)

[sinophile]

Solve for 0<theta<360:

My solution:
sec^2(theta)=4/3
1/cos^2(theta)=4/3
cos^2(theta)=3/4
cos(theta)=plus-or-minus sqrt(3/4)

Related angle= cos^-1(plus-or-minus 3/4)
approx. =41 degrees
Therefore theta= 41, 139, 221, 319.

Textbook solution:
theta=30, 150, 210, 330.

Why is my solution different from the textbook one? Did I do something wrong?

 

[clintmyster]

Solve for 0<theta><360:

My solution:
sec^2(theta)=4/3
1/cos^2(theta)=4/3
cos^2(theta)=3/4
cos(theta)=plus-or-minus sqrt(3/4)

Related angle= cos^-1(plus-or-minus 3/4)
approx. =41 degrees
Therefore theta= 41, 139, 221, 319.

Textbook solution:
theta=30, 150, 210, 330.

Why is my solution different from the textbook one? Did I do something wrong?

maybe you didnt sqrroot the whole thing

your solutions should be cos^-1 (+- root3/2)
</theta>

 

[lyounamu]

Solve for 0<?xml:namespace prefix = theta<360 /><theta<360:< p>
My solution:
sec^2(theta)=4/3
1/cos^2(theta)=4/3
cos^2(theta)=3/4
cos(theta)=plus-or-minus sqrt(3/4)

Related angle= cos^-1(plus-or-minus 3/4)
approx. =41 degrees
Therefore theta= 41, 139, 221, 319.

Textbook solution:
theta=30, 150, 210, 330 within given domain

presumable 0 <= x <= 360

Why is my solution different from the textbook one? Did I do something wrong?

sec^(@) = 4/3
cos^2(@) = 3/4
cos @= +- sqrt(3)/2
@ = 30, 150, 210 and 330

</theta<360:<>