.
Solve the following Trigonometric quadratic equations for all angles from 0<= X < 360 to the nearest degree
1) 4tan^2(x) +3tan(x ) -1=0 and 2) 6sin(x) +3 =2csc(x)
Please Help Me...
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Please listen me very attentively . . .
Introduce new variable y = tan(x). Then your original equation takes the form
= 0. (1)
Solve it by applying the quadratic formula:
= 
= 
= 
.
So, the equation (1) has two solution.
1. 
= 
= 
= 
====> tan(x) = ====> x = 
AND/OR x = 
.
2. 
= 
= 
====> tan(x) = -1 ====> x = 
= 
AND/OR x = 
= 
.
Answer. There are 4 solutions: x = , x = , x = , x = .
Introducing new variable is the standard way to solve such problems.
For more examples see the lessons
- Solving simple problems on trigonometric equations
- Solving typical problems on trigonometric equations
- Solving more complicated problems on trigonometric equations
- Solving advanced problems on trigonometric equations
- OVERVIEW of lessons on calculating trig functions and solving trig equations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".
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I know that in 5 minutes other tutors will come explaining that you can factor the equation (1) or even factor the original equation
instead of using the quadratic formula.
It is possible, of course. But regarding factoring, you must know this
It works smoothly in two cases: a) you can easily factor it mentally,
b) you know the answer in advance (may be, based on your previous experience).
This is why I prefer to use quadratic function in such cases:
It is universal and works ALWAYS.
H A P P Y L E A R N I N G !!
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One more advise: do not put more than one problem/one question to your post.
By violating this rule, you work against yourself . . .
