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How would I find the cosine (150) without using a calculator?

 Jun 14, 2014

Best Answer 

 #2
avatar+118703 
+6

150 degrees is 2nd quad which means the cosine of it is negative.

Now just look at the acute angel equivalent 180-150=30degrees.

I do not memorise these ratios.  I draw an equilateral triangle of side legth 2 and then bisect it like in the diagram.

I then worry only about one half of it.  The bottom is 1 unit. The hypotenuse is 2 units.  Using pythagoras' Theorum you get the height as sqrt(3)

Cos1500=cos300=32

 Jun 15, 2014
 #1
avatar+130466 
+6

Well, you have to remember that this is just a 30° angle in the second quadrant. And the cos(30°) = √3/2.

But, since the cosine is negative in this quadrant, we have to take the negative value of this = -√3/2.

And that's it.....

 

 Jun 15, 2014
 #2
avatar+118703 
+6
Best Answer

150 degrees is 2nd quad which means the cosine of it is negative.

Now just look at the acute angel equivalent 180-150=30degrees.

I do not memorise these ratios.  I draw an equilateral triangle of side legth 2 and then bisect it like in the diagram.

I then worry only about one half of it.  The bottom is 1 unit. The hypotenuse is 2 units.  Using pythagoras' Theorum you get the height as sqrt(3)

Cos1500=cos300=32

Melody Jun 15, 2014

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