The first three trigonometric functions are sine, cosine, and tangent.
When we find the sine, cosine, and tangent of different angles, we will use letters to name the alphabet. Sometimes we will say, "Find sin A." That just means to find the sine of the angle labeled A. We may also use letters from the Greek alphabet. Theta is the most common..
Let's start with sine (abbreviated "sin"). Following the link to view step-by-step instructions on finding the sine of an angle. Click on the video to watch a teacher explain the sine of an angle. Once you feel like you've seen enough, try some examples for yourself!!! Your goal: complete five (5) sine computations correctly. You may have to use the Pythagorean Theorem before you can solve for sine.
How did you do with sine? The second trigonometric function is cosine (abbreviated "cos"). Try to get five (5) of these examples correct once you've learned the pattern of cosine. Will you need to use the Pythagorean Theorem again? Most definitely.
If you've gotten sine and cosine, you've conquered the biggest part. The last of our first three trigonometric functions, tangent, is a combination of the first two. Just like the first two, click here to learn about tangent (abbreviated "tan"). Don't forget to copy what you learn in your notebook, so you'll have it to reference later. Can you get five (5) tangent computations correct at the end? Be sure to let your teacher know how many of each you got correct!
SINE, COSINE, AND TANGENT!!!
HERE'S A FUN WAY TO REMEMBER THEM:
SINE = OPPOSITE / HYPOTENUSE
COSINE = ADJACENT / HYPOTENUSE
TANGENT = OPPOSITE / ADJACENT
Click on the picture to take a test over all three of the trigonometric functions.
Still stuck? Try this!!!!
At the beginning of this WebQuest, we reviewed reciprocals. Now, you know the three basic trigonometric functions. Together with your partner or small group, you will complete this WebQuest.
Here are the three basic trigonometric functions one more time:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Now, here are the names of the reciprocal functions:
The reciprocal of sine (sin) is cosecant (csc).
The reciprocal of cosine (cos) is secant (sec).
The reciprocal of tangent (tan) is cotangent (cot).
YOUR JOB: Together with your partner or small group, write down what the reciprocal functions would look like in terms of opposite, adjacent, and hypotenuse. Do it WITHOUT consulting a textbook, website, or other resource!!! Just like the three basic trig functions, list the reciprocal functions:
csc θ = __________ / ____________
sec θ = __________ / ____________
cot θ = __________ / ____________
Once you all have it, and you think you agree, click here to check your answers!
Did you get it? Are you a trig master now? Here's your chance to show your stuff. Choose one of the following ways to show you're a master:
1) Create your own "trig functions" video. Be as creative as you would like - just make sure you are also appropriate. You can use the video in the introduction as a guide. Make sure you use your math vocabulary and get the trigonometric functions correct!!!
2) In your own words, explain each of the six trigonometric functions you have just learned. Again, make sure you use your math vocabulary and get the trigonometric functions correct!!!