Questions asked by Mibo

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• Sin^2(x)-cos^2(x)= sin^2(x)+cos^2(x) Find exact solutions between 0 and 2π How should I solve this?
  
• If sin(x) = 0.4 , what is sin((3π/2)+x)=? , Show exact values. How would I get along solving this without a calculator.
  
• What is sin(4x) in terms of sin(2x) and cos(2x)?
  
• Why does #tan(x+(pi/2))=cot(x)#? or #cos((pi/2)-x)=sin(x)# and is it like that with #(3pi)/2# as well?
  
• Water is being poured into a cylindrical vase at a rate of 15 millilitres per second. If the radius of the vase is 10 cm, find the rate with which the height of water in the vase is rising. ?
  
• A lottery claims that 10% of tickets win a prize. How many tickets should you purchase to be more than 50% sure of winning a prize?
  
• Given #z# is a complex number such that #Arg(z) = theta# and #|z| = r# , write an expression for each of #Arg(4z^3)# and #|4z^3|# in terms of r and/or θ. How should I approach this?