SOLUTION: Find all solutions for the following equations.Record your answer in exact form where possible.
(a) {{{2}}}{{{"cos"^2x}}}{{{""=""}}}{{{-3}}}{{{"sin"}}}{{{x}}}
(b) {{{"sin"}}}{{{x
Algebra ->
Trigonometry-basics
-> SOLUTION: Find all solutions for the following equations.Record your answer in exact form where possible.
(a) {{{2}}}{{{"cos"^2x}}}{{{""=""}}}{{{-3}}}{{{"sin"}}}{{{x}}}
(b) {{{"sin"}}}{{{x
Log On
You can put this solution on YOUR website! Find all solutions for the following equations.Record your answer in exact form where possible.
(a)
(b)
Thinking I may have to us Half-angle formula on these (not sure)
No you don't need those.
Use the identity: written as to rewrite the left side:
Get 0 on the right:
Rearrange terms on the left in descending order:
To make factoring easier, multiply through by -1
Setting the first factor = 0
This is impossible because no sine can be greater than 1 or
less than -1.
Setting the second factor = 0
All angles in QIII and QIV with reference angle 30° (or
if your teacher wants radians) are solutions.
In degrees:
;
In radians:
;
--------------------------------
--------------------------------
--------------------------------
Get 0 on the right:
Factor out on the left side:
Setting the first factor = 0
All angles with reference angle 0 are solutions:
In degrees:
In radians:
;
Setting the second factor = 0
All angles in QI and QIII with reference angle 45° (or
if your teacher wants radians) are solutions.
In degrees:
;
In radians:
;
Edwin
