Is Cos(60) Equal to Cos(-60)? Examining the Trigonometric Identity

  • Thread starter Thread starter The_Prime_Number
  • Start date Start date
AI Thread Summary
Cos(60) is equal to cos(-60) because cosine is an even function, meaning cos(-x) equals cos(x). Both angles, 60 degrees and -60 degrees, correspond to the same x-coordinate on the unit circle, which is positive. Therefore, cos(60) and cos(-60) yield the same value. This equality holds true for any angle where the cosine function is evaluated. Understanding this concept clarifies the relationship between these angles in trigonometry.
The_Prime_Number
Messages
3
Reaction score
0
I was thinking about this, and wanted to know if it was true...

-cos(60) = cos(-60) = cos(300) = cos(60)
 
Physics news on Phys.org
no its not,

cos(-x) = cos(x) ( cos is an even function )

If you draw these angles over the unit circle, then cos(x) refers to the x component of where the ray intersects the circle. For 60 degrees and -60 degrees, the x component lies to the right of the y axis, so both are positive (and equal).
 
Ok, thanks for clearing that up for me.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top