After you have finished constructing the spaghetti sine curve, answer the following questions.
What is the radius of the circle? 5in
What is the circumference of the circle? 2πr=2(π)(5)=31.4
At what degree measure on your circle would you find the angle correponding to 375°? 15 degrees What is the term for the angle you found in question #3? reference angle
After how many degrees does the graph start to repeat? 360 degrees This is the period of the graph and corresponds to one complete wave – a wavelength.
What is the height of the triangle (spaghetti) at 30 degrees? Compare this to the radius (that it, find the ratio: [pic]and make it a decimal). 2.5/5=.5 On the calculator find the sine of 30º: .5 How does that compare to your answer above for [pic]?
it is the same
What is the height of the triangle at 150° and 330°? 2in. How does this compare with the height of the 30° angle in #6 above? it is the same.
What is the height of the triangle at 45°, 135°, 225°? 3.5in. Make a ratio of for these angles like you did in #6: 3.5/5=.7 On the calculator find the sine of 45°: .707 Compare this to your answer to question #9.
this is very close
If you were to explain to a person who has never seen trigonometry what the sine of an angle is, what would you tell them?
I would tell them that it is the side opposite of the angle over the hypotenuse which is the radius of the circle.
12. What do you think is the significance of reference angles?
If you know the main reference angles than you can use that information to find other angles on the circle. -----------------------
Draw the x and y axis on your circle.
With a protractor put a mark every 15° and extend these marks from the origin to the edge of the circle. Take a string and wrap it carefully around the circumference of your circle. Put a mark on the string at all of your 15° intervals. Take the string and...