Melody

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Melody  Feb 11, 2022
 #1
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+10

think about the first quadrant of a unit circle..

The unit circle is the circle with a radius of 1 and a centre of (0,0)

 

The fist quadrant covers angles 0 to pi/2.   

At first only consider proper acute angles. 

 

You should watch this video - it is very good.   :)

 

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

 

 

---------------------------------------------------

 

$$\\cos \theta = \frac{adj}{hyp}\\\\
$but the hypotenuse is the radius of the circle so it is 1$\\\\
so\\
cos \theta = \frac{x}{1}=x\\\\
$By the same type of logic you can see that$\\\\
sin\theta = y$$

 

now just follow this for all angles.

With regards to the unit circle.   

  $$cos\theta$$  is given by the x value 

and

$$sin\theta$$     is given by the y value.

 

 

If you develope a good understanding of the unit circle and what it represents senior trig will be easier.

Mar 17, 2015
 #1
avatar+118735 
+5
Mar 16, 2015
 #463
avatar+118735 
+8

@@ End of Day Wrap   Mon 16/3/15     Sydney, Australia Time   10:25 pm     ♪ ♫

 

Good evening,     (๑‵●‿●‵๑)

 

Our magnificent answerers today were Gibsonj338, Shaomada, CPhill, Alan, Heureka, Bertie and Rosala.

A great big thank you to each of you.       

 

Interest Posts:

 

1)    What is the difference between a cat and a comma?     Thanks anon.

2)    Solving a difficult inequality                 Thanks  Melody and CPhill

3)    Tricky trig derivative.                          Thanks Melody and CPhill

4)    Geometry                                          Not answered.

  

               ♫♪  ♪ ♫                                ♬ ♬ MELODY ♬ ♬                                 ♫♪  ♪ ♫

Mar 16, 2015