English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

Solve For Θ

0 ≤ Θ < 360

2007-08-05 07:03:40 · 3 answers · asked by Bobby 1 in Science & Mathematics Mathematics

Still Need More Help

Please

2007-08-05 07:45:01 · update #1

3 answers

tan² θ + 1 = sec² θ
sec ² θ = sec θ
1 / cos ² θ = 1 / cos θ
cos θ = cos ² θ
cos ² θ - cos θ = 0
cos θ (cos θ - 1) = 0
cos θ = 0 , cos θ = 1
θ = 90° , 270° , 0°

2007-08-05 08:06:49 · answer #1 · answered by Como 7 · 0 1

tan²Θ +1 = secΘ

sec²Θ = secΘ

We want to divide by secΘ, which we can do unless secΘ=0. But secant is always either >1 or < -1, so it's okay to divide by it. Thus:

secΘ=1, meaning 1/cosθ=1

But then cosθ=1 too.

So we want the point(s) where secΘ=1, which are also where cosΘ=1. The only such point from 0≤Θ<360 is Θ=0 degrees.

Please do not trust the other user below, who tells us that we want cosΘ = 0. If cosΘ=0, then secΘ is not defined and the equation is not valid. Thus he has my solution (Θ=0) and two solutions that are invalid.

You see, in his algebra, he goes from:
1/cos²Θ = 1/cosΘ

to:
cos²Θ = cosθ

However, that step involves multiplying both sides by cosΘ. If cosΘ=0, then he just multiplied both sides by zero, not to mention he would initially have:

1/0 = 1/0

Neither quantity is defined, and thus cosΘ=0 is definitely not allowed.

2007-08-05 07:12:05 · answer #2 · answered by сhееsеr1 7 · 0 0

This answer is fake. in any different case, the two the equation is written incorrectly in any different case there is extra techniques in the priority that wasn't secure in the define you wrote. Double verify which you typed the priority wisely and which you secure each and all of the techniques that became given in the priority.

2016-11-11 07:12:10 · answer #3 · answered by ? 4 · 0 0

fedest.com, questions and answers