Graphing Sine and Cosine

Graphing sine and cosine functions is fundamental in understanding periodic phenomena and wave behavior. These functions, originating from trigonometry, depict the oscillatory motion commonly found in nature, such as sound waves, light waves, and mechanical vibrations. By plotting sine and cosine waves on a coordinate plane, one can visually grasp their periodic nature, amplitude, phase shifts, and frequency. Through precise manipulation of parameters, such as frequency and amplitude, these graphs serve as powerful tools in fields like physics, engineering, and signal processing, enabling analysts to model and predict various cyclic phenomena with accuracy and insight.

Questions
  • What is the smallest value of #y=cos x#?
  • How do you solve: sin(π/2-x)/cos(π/2-x) ?
  • What does the graph of #f(x) = (sin^3x + sinxcos^2x)/sinx# look like?
  • What is the period of #y=cos x#?
  • How do you graph #y=cos(2x)+1#?
  • What is the graph of #y=sin (x/3)#?
  • What is the graph of #y=sin(x+30)#?
  • What is the graph of #y=sin(x/2)#?
  • What is the amplitude of the graph of #y = sin x#?
  • What is the range of the graph of #y = sin x#?
  • What are the x-intercepts of the graph of #y = cos x#?
  • What is the maximum value that the graph of #y=cos x# assumes?
  • What is the range of the graph of #y = cos x#?
  • What is the y-intercept of the graph of #y = cos x#?
  • What is the graph of #y=cos(x-pi/2)#?
  • How do I graph #y=cos(x-π/4)#?
  • What is the period of #y=3 cos 5x#?
  • What is the maximum value of the function #h(x)=2cos(10x)+12#?
  • If 2#cos^2x# - #cosx# = 1 , what is the value of #x#?
  • If 1 + #cosx# - 2#sin^2x# = 0 , what is the value of #x#?