Solution 4.4:3c - Förberedande kurs i matematik 1

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                      1. Numerical calculations
                       
                        1.1 Different types of numbers 
                        1.2 Fractions 
                        1.3 Powers
                      
                    
                      2. Algebra
                       
                        2.1 Algebraic expressions 
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                      3. Roots and logarithms
                       
                        3.1 Roots 
                        3.2 Equations with roots 
                        3.3 Logarithms 
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                      4. Trigonometry
                       
                        4.1 Angles and circles 
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                        4.3 Relations 
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+			Solution 4.4:3c
			
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- {{NAVCONTENT_START}} + If we consider the entire expression <math>x + 40^{\circ}</math> as an unknown, we have a basic trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for <math>0^{\circ}\le x+40^{\circ}\le 360^{\circ}</math> namely <math>x+40^{\circ} = 65^{\circ}</math> and the symmetric solution <math>x + 40^{\circ} = 180^{\circ} - 65^{\circ} = 115^{\circ}\,</math>.
- <center> [[Image:4_4_3c.gif]] </center> + 
- {{NAVCONTENT_STOP}} + 
-   + 
  
 [[Image:4_4_3_c.gif|center]]  [[Image:4_4_3_c.gif|center]]
  + 
  + It is then easy to set up the general solution by adding multiples of <math>360^{\circ}\,</math>,
  + 
  + {{Displayed math||<math>x + 40^{\circ} = 65^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x + 40^{\circ} = 115^{\circ} + n\cdot 360^{\circ}</math>}}
  + 
  + for all integers ''n'', which gives
  + 
  + {{Displayed math||<math>x = 25^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x=75^{\circ} + n\cdot 360^{\circ}\,\textrm{.}</math>}}
Current revision
If we consider the entire expression \displaystyle x + 40^{\circ} as an unknown, we have a basic trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for \displaystyle 0^{\circ}\le x+40^{\circ}\le 360^{\circ} namely \displaystyle x+40^{\circ} = 65^{\circ} and the symmetric solution \displaystyle x + 40^{\circ} = 180^{\circ} - 65^{\circ} = 115^{\circ}\,.


It is then easy to set up the general solution by adding multiples of \displaystyle 360^{\circ}\,,





\displaystyle x + 40^{\circ} = 65^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x + 40^{\circ} = 115^{\circ} + n\cdot 360^{\circ}


for all integers n, which gives





\displaystyle x = 25^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x=75^{\circ} + n\cdot 360^{\circ}\,\textrm{.}



Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.4:3c"
@@ Line 1: / Line 1: @@
-{{NAVCONTENT_START}}
+If we consider the entire expression <math>x + 40^{\circ}</math> as an unknown, we have a basic trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for <math>0^{\circ}\le x+40^{\circ}\le 360^{\circ}</math> namely <math>x+40^{\circ} = 65^{\circ}</math> and the symmetric solution <math>x + 40^{\circ} = 180^{\circ} - 65^{\circ} = 115^{\circ}\,</math>.
-<center> [[Image:4_4_3c.gif]] </center>
-{{NAVCONTENT_STOP}}
 [[Image:4_4_3_c.gif|center]]
+It is then easy to set up the general solution by adding multiples of <math>360^{\circ}\,</math>,
+{{Displayed math||<math>x + 40^{\circ} = 65^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x + 40^{\circ} = 115^{\circ} + n\cdot 360^{\circ}</math>}}
+for all integers ''n'', which gives
+{{Displayed math||<math>x = 25^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x=75^{\circ} + n\cdot 360^{\circ}\,\textrm{.}</math>}}
 \displaystyle x + 40^{\circ} = 65^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x + 40^{\circ} = 115^{\circ} + n\cdot 360^{\circ}
 \displaystyle x = 25^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x=75^{\circ} + n\cdot 360^{\circ}\,\textrm{.}