document.write( "Question 814275: Hi, my math book says that cos (-feta) = +cos feta\r
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Algebra.Com's Answer #490201 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
This is not a formal proof but I think it will give you the idea. Draw a picture:
  1. Draw a first quadrant angle. Let's call it \"A\".
  2. On the same graph draw the negative of the first quadrant angle (into the 4th quadrant). We'll call it B.
    3. From anywhere on the terminal side of angle A, draw a perpendicular towards the x-axis and continue on through to the terminal side of B.
  3. The terminal side of angle A, the perpendicular to the x-axis and the portion of the x-axis up to where the perpendicular hits the x-axis form a right triangle.
  4. The terminal side of angle B, the perpendicular to the x-axis and the portion of the x-axis up to where the perpendicular hits the x-axis form another right triangle.
  5. The two triangles are congruent. So all the pairs of corresponding sides are congruent to each other, except the vertical sides. (The vertical side of the triangle in the first quadrant is up (positive) and the vertical side of the triangle in the fourth quadrant is down (negative).
  6. Since cos is adjacent over hypotenuse and since the adjacent and hypotenuse sides of the two right triangles are congruent: \"cos%28-theta%29+=+cos%28theta%29\"
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