Welcome to Exploring trig functions! This is intended to give you a chance to see how trig functions are related and maybe discover some new trig identities. [br]Use the questions below as a guide if you like, or feel free to explore and experiment on your own!

1. Make sure that "Show Sum of Checked Funtions" is checked. Experiment with different combinations of functions and their exponents (the sliders on the left) and try to see how many ways you can make the sum a constant function of 1. What about other constant functions? Do you have any strategies that you're using?[br][br]2. Find a pair of functions such that their sum (the red function) looks like it might be a transformation of one of the base trig functions. (For example, (sin(x))^4-(cos(x))^4 looks like a transformation of a cosine function to me.)[br]Select the "Custom Function" button and try to see if you can find a transformation of just one trig function that's the same as your sum of functions. Congratulation! You've found a trig identity! [br][br]3. Now, uncheck "Sum of checked fucntions." Can you find a pair of trig functions that you can make equal just by changing the exponents? How are the exponents of the two functions related when you make them equal? What do you notice about the pairs of functions this works for? (Hint: Think about which ratios of side lengths on a right triangle each function corresponds to. For example, sin(x)=opposite/hypotenuse and cot(x)=adjacent/opposite.)