How to Solve Using Trigonometric Identities

"Real World" Application Problems

  1. You are a knight that has been hunting down a renegade dragon for some time and as you camp, you remember an equation defining where a renegade dragon will fly based on the amount of rainfall. The equation is defined as 1/(sec2(X)+csc2(X))-1+R=sec2(X)+sin(X) where R=the amount of rain(in inches under 1 inch) and X is the angle of flight. You figure you can use this info to lay a trap for the beast and end the threat. you figure that there has been about 1/2" of rain. You also know that the dragon likes watching the sunrise.  What direction is the dragon flying? 
  2. You are playing a game of Munchkin when you draw a card that says you will die from random anvil falls if you don't solve the Problem of the MatheMagician, which is as follows: 1/csc2(X)+1/sec2(X)-tan2(X)+(cos(90°-X))2=1+tan2(X)-csc2(90°-X)+√2/2
  3. As you are going along your daily business, a man walks up to you and hands you a note containing a problem. The man says that if you solve it, you will get a Golden Apple and a million bucks. So you solve the problem. [0°,360°) sin2(X)+cos2(X)=-1


  1. EN30°
  2. 45°+360k°, 135°+360k°, 225°+360k°, 315°+360k°
  3. Trick Question, there is no answer. Nothing squared equals a negative unless there is i, and trig doesn't use i as it is based on a graph called the Unit Circle.