Exact value Precalc review

Question

Give the EXACT value of the following.

 

a)sin 135

b)cos 240

c)tan 330

 

i missed this unit seems easy though. I would assume you just type that into a calculator? But that seems too simple .

 

much appreciated!

Answer 1

We use the addition and subtraction of angles identities for sine and cosine.

 

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

sin(x - y) = sin(x)cos(y) - cos(x)sin(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

 

 

a)

 

sin(135)

 

Identity two angles that give a sum of or difference of 135, but you can easily identity sine and cosine of.

 

90 and 45 add up to 135.  The sine and cosine of these angles are obvious to us.

 

sin(135) = sin(90 + 45)

             = sin(90)cos(45) + cos(90)sin(45)

             = 1 * √(2) / 2   +  0 * √(2) / 2

             = √(2) / 2

 

Now that you know the concept.  Try the last two. 

 

Answer 2

b) 240^o is 60^o past 180, giving us a 30-60-90 triangle in the 3rd quadrant.

 

cos 60^o = 1/2  but cosine is negative in Q3 so cos240^o = -1/2

 

c) 330^o is 30^o short of 360^o .  Again, a 30-60-90 triangle.  

 

tan 330^o = -1/√3  = -√3/3

 

   -√3

= -----

     3