Question 395390: Hi, please help me solve this problem:
Is this true of false: If alpha and beta are in standard position and are coterminal, then cos alpha must equal cos beta.
Thanks!
Found 2 solutions by jim_thompson5910, richard1234:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Recall that coterminal angles x and y are of the form  for some integer k. For example, say x=20 and k=2, then  . So x=20 and y=740 are coterminal angles.
So if  and  are coterminal angles, then 
Now take the cosine of both sides to get 
 Expand the right side.
Note: since k is an integer (ie whole number), this means that numbers of the form 360k are: 360, 720, ... So this means that the cosine of 360k is 1. Why? We can easily show that cos(360*2)=cos(360+360)=cos(360)cos(360)-sin(360)sin(360)=1*1-0*0=1. So cos(360*2)=cos(360). We can extend this infinitely, which means that cos(360k)=1. The same idea applies to sine as well. So sin(360k)=0
 Evaluate the cosine and sine of 360k to get 1 and 0 (see explanation above)
 Multiply
 Combine like terms.
So because we've shown that , this means that the statement is true.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
Answer by richard1234(7193)  (Show Source):
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