G.4.6.2 New Names, Same Ratios

For this activity you'll need a calculator - you can use one you have at home or use desmos.com. Let's pause and make sure everyone has access to a calculator and that it is in "degree" mode.
  • On some handheld calculators have a "mode" button, push it and then find "degrees" instead of "radians."
  • On some handheld calculators there is a button with "DRG" on it - press it until "Deg" appears on your screen.
  • The calculator on your phone is difficult to use for trig functions, I recommend avoiding it.
  • In desmos click the wrench button in the upper right corner and click on Degrees (so it is green):


Here are the triangles and ratios we found in the last activity.

Use your calculator to determine the following values: sin(37°) cos(37°) tan(37°)

Use your calculator to determine the following values: sin(72°) cos(72°) tan(72°)

For every single acute angle (1° - 89°) of a right triangle, someone has written down the ratios of the sides. In "olden times" we had to use a table like this to solve all of the problems that we're going to see in unit 4. Luckily, "nowadays" these values are stored in our calculators. Mathematicians like shortcuts, so instead of saying "opposite side divided by the hypotenuse" we use the nickname sine (abbreviated as sin). The other 2 ratios also have nicknames as well...cosine (cos) is "adjacent side divided by hypotenuse," and tangent (tan) is "opposite side divided by adjacent side."