Difference between revisions of "Angles"

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==Examples==
 
==Examples==
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Convert the following from degrees to radians or radians to degrees
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Convert the following from degrees to radians or radians to degrees. It is usually understood that if an angle has a <math> \pi</math> in it the angle measure is given in radians.
  
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<math>1.\, 245^\circ</math>
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<math>a)\, 245^\circ</math>
  
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<math>2. \, \dfrac{5\pi}{4}</math>
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<math>b) \, \dfrac{5\pi}{4}</math>
  
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<math>3.\, 275^\circ </math>
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<math>c)\, 275^\circ </math>
  
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<math>4. \, \dfrac{9\pi}{2} </math>
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<math>d) \, \dfrac{9\pi}{2} </math>
  
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<math>5. \, 30^\circ </math>
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<math>e) \, 30^\circ </math>
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'''Solutions'''
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To convert from degrees to radians, we multiply the degrees by <math> \dfrac{\pi}{180}</math>. To convert in the other direction, radians to degrees, we multiply the radians by <math> \dfrac{180}{\pi}</math>
 +
<math> a) \dfrac{245 \pi}{180} = \dfrac{49*5\pi}{36*5} = \dfrac{49 \pi}{36}</math>
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<math> b) \dfrac{ 5\pi}{4}* \dfrac{180}{\pi} = \dfrac{180*5}{4} = \dfrac{4*45*5}{4} = 45*5 = 225</math>
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<math> c) \dfrac{275 \pi}{180} = \dfrac{55*5\pi}{36*5} = \dfrac{55 \pi}{36}</math>
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<math> d) \dfrac{9 \pi}{2} * \dfrac{ 180}{\pi} = 90*9 = 810</math>
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<math> e) \dfrac{30 \pi}{180} = \dfrac{\pi}{6}
  
 
   [[Math_5|'''Return to Topics Page]]
 
   [[Math_5|'''Return to Topics Page]]

Revision as of 14:01, 27 March 2016

Angles

The main things to remember about angles is that they are measured starting from the positive x-axis, unless otherwise stated, and measured in a counter-clockwise direction.

We say that a whole revolution is 360 degrees, making an arrow pointing north a 90 degree angle, west a 180 angle, and south a 270 degree angle.


Radians

If we have an angle in degrees and we want the angle measure in radians we can use the conversion facto of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 180^\circ = \pi \text{ radians}} This means that if we want to convert back and forth Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \qquad 1 \text{ radian } = \frac{180}{\pi} \text{ degrees}}

Examples

Convert the following from degrees to radians or radians to degrees. It is usually understood that if an angle has a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi} in it the angle measure is given in radians.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a)\, 245^\circ}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b) \, \dfrac{5\pi}{4}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c)\, 275^\circ }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d) \, \dfrac{9\pi}{2} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e) \, 30^\circ }

Solutions To convert from degrees to radians, we multiply the degrees by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dfrac{\pi}{180}} . To convert in the other direction, radians to degrees, we multiply the radians by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dfrac{180}{\pi}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a) \dfrac{245 \pi}{180} = \dfrac{49*5\pi}{36*5} = \dfrac{49 \pi}{36}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b) \dfrac{ 5\pi}{4}* \dfrac{180}{\pi} = \dfrac{180*5}{4} = \dfrac{4*45*5}{4} = 45*5 = 225}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c) \dfrac{275 \pi}{180} = \dfrac{55*5\pi}{36*5} = \dfrac{55 \pi}{36}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d) \dfrac{9 \pi}{2} * \dfrac{ 180}{\pi} = 90*9 = 810}

<math> e) \dfrac{30 \pi}{180} = \dfrac{\pi}{6} 

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