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the graph of y = sin x and the line y = (-1)/2 over the interval [0 degree, 360 degree]. Where do the two graphs intersect? Give exact answers in degrees

Guest May 20, 2015

Best Answer 

 #1
avatar+20022 
+10

the graph of y = sin x and the line y = (-1)/2 over the interval [0 degree, 360 degree]. Where do the two graphs intersect? Give exact answers in degrees

$$\small{\text{$ \begin{array}{rcl|rcl}\sin{(x_1)} &=& -\frac12 \qquad & \qquad \sin{(x_1)} &=& \sin{ (180\ensurement{^{\circ}} -x_2) } =-\frac12 \\&&&\\ x_1 &=& \arcsin{( -\frac12 )} \qquad & \qquad \sin{ (180\ensurement{^{\circ}} - x_2) } &=&-\frac12 \\&&&\\x_1 &=& -30\ensurement{^{\circ}} + 360\ensurement{^{\circ}} =330\ensurement{^{\circ}} \qquad & \qquad 180\ensurement{^{\circ}} - x_2 &=& \arcsin(-\frac12) \\&&&\\&& &\qquad x_2 &=& 180\ensurement{^{\circ}}-\arcsin{( -\frac12 )} \\&&&\\&&\qquad & x_2 &=& 180\ensurement{^{\circ}} +30\ensurement{^{\circ}} \\&&&\\&&\qquad & x_2 &=& 210\ensurement{^{\circ}}\\\end{array}$}}$$

heureka  May 20, 2015
 #1
avatar+20022 
+10
Best Answer

the graph of y = sin x and the line y = (-1)/2 over the interval [0 degree, 360 degree]. Where do the two graphs intersect? Give exact answers in degrees

$$\small{\text{$ \begin{array}{rcl|rcl}\sin{(x_1)} &=& -\frac12 \qquad & \qquad \sin{(x_1)} &=& \sin{ (180\ensurement{^{\circ}} -x_2) } =-\frac12 \\&&&\\ x_1 &=& \arcsin{( -\frac12 )} \qquad & \qquad \sin{ (180\ensurement{^{\circ}} - x_2) } &=&-\frac12 \\&&&\\x_1 &=& -30\ensurement{^{\circ}} + 360\ensurement{^{\circ}} =330\ensurement{^{\circ}} \qquad & \qquad 180\ensurement{^{\circ}} - x_2 &=& \arcsin(-\frac12) \\&&&\\&& &\qquad x_2 &=& 180\ensurement{^{\circ}}-\arcsin{( -\frac12 )} \\&&&\\&&\qquad & x_2 &=& 180\ensurement{^{\circ}} +30\ensurement{^{\circ}} \\&&&\\&&\qquad & x_2 &=& 210\ensurement{^{\circ}}\\\end{array}$}}$$

heureka  May 20, 2015
 #2
avatar+93616 
+5

Thanks Heureka,

 

Here is the graphical solution

https://www.desmos.com/calculator/p5ia0okfnz

Melody  May 20, 2015

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