Homework Help Forum: Trig

Posted by Trig on Tuesday, November 3, 2009 at 8:27pm.

How come cosine of 225 degrees is a positive number i thought it was negative because it's reference angle would be 45 degrees below the second quadrant and in a unit circle cosine is just the x value so I thought cosine of something in both the second and third were negative apparently i'm wrong please explain

• Trig - Reiny, Tuesday, November 3, 2009 at 8:33pm

  225º is in the fourth quadrant, 45º below the first quadrant, so its x value is indeed positive. Check how angles are measured.

  
  

• Trig - Trig, Tuesday, November 3, 2009 at 8:34pm

  I think i was in radians my bad um how come tan of 300 is negative root three tangent in unit circle is y/x I am getting .5/(root three/2) which is not root three

  
  

• OOPS -Trig - Reiny, Tuesday, November 3, 2009 at 8:36pm

  Forget about my previous post. Obviously 225º is in the third quadrant, 45º below the second quadrant like you said. So of course cos 225 is negative.

  
  

• Trig - Reiny, Tuesday, November 3, 2009 at 8:38pm

  tan 300º = -tan 60º by the CAST rule = -√3/1 from the ratios of the 30-60-90 triangle = -√3

  
  

• Trig - Trig, Tuesday, November 3, 2009 at 8:44pm

  why wouldn't you use the 30 degree angle? I did 360 -90 to get 270 degrees and then did 300 - 270 to get 30 degrees and used that angle why would I use the 60 degree angle instead of the thirty

  
  

• Trig - Reiny, Tuesday, November 3, 2009 at 9:03pm

  Always ask yourself, "How far away from the x-axis am I "? to get the reference angle. e.g. sin 160 160º is 20º away from the x-axis and according to the CAST rule in quadrant II the sine is positive, so sin 160º = sin 20º e.g. tan 310º 310º is 50º from the x-axis and according to the CAST rule, in quadrant IV the tangent is negative, so tan 310 = -tan 50 check my examples with your calculator

  
  

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