SOLUTION: 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!

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): You can put this solution on YOUR website!
Co-terminal angles have the same coordinate (x,y) in the unit circle, so all respective trigonometric functions are the same.
RELATED QUESTIONS
Hi, please help me solve this problem: Is this true of false: If alpha and beta are in (answered by richard1234)
Please help me solve this problem: Is this true of false: if alpha and beta are in... (answered by stanbon)
Please help me solve this question If alpha and beta are 2 positive acute angles... (answered by ikleyn)
Hi, please help me solve this problem: Suppose sec alpha = -7/4 and that the terminal... (answered by stanbon,lwsshak3)
Please help me solve this problem: Suppose that cot (Beta)= 9/7 and Beta is not in... (answered by richard1234)
Hi, please help me solve this problem: Verify the identity of csc alpha - (cos... (answered by richard1234)
Hi, please help me solve this problem: Suppose sec alpha = 7/2 and alpha is in... (answered by ewatrrr)
Hi, please help me solve this problem: Using proper notation, describe ALL angles that (answered by stanbon)
Can someone please help me with this question?! Thank you! If cos(alpha)=0.228 and... (answered by greenestamps)