How is tangent related to sine and cosine

Try It Out Ready to keep learning? Check out the activities below with help from a friend or family member! Learn more about sine, cosine, and tangent, and look at some helpful diagrams on the Math Is Fun website. Did this help you gain a deeper understanding of these functions? Now that you have a mnemonic to help you remember the formulas for sine, cosine, and tangent, make a poster that would help others remember.

Be sure to include the correct formulas as well! Feeling crafty? Learn more about geometric shapes and get creative by making your own! You can try to make some shapes on your own or follow along with this video to learn to make 3D shapes with just paper and a pair of scissors. Make sure an adult helps you, and have fun creating your shapes.

Did you get it? Test your knowledge. Wonder Words branches angles label functions formulas measurements trigonometry geometry mathematicians Take the Wonder Word Challenge. Join the Discussion. Related Wonders for You to Explore Match its definition: plural something such as a quality or measurement that is related to and changes with something else. Word Match Congratulations! Share results. Play Again Quit. Next Question. See your results. Share Results. Divide the length of one side by another side.

Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. You can read more about sohcahtoa Move the mouse around to see how different angles in radians or degrees affect sine, cosine and tangent. In this animation the hypotenuse is 1, making the Unit Circle. If we incline the 8 foot ladder so that its base is 6 feet from the wall, the angle decreases to about As you can see, for every angle, there is a unique point on the ground that the 8 foot ladder touches, and it is the same point every time we set the ladder to that angle.

Mathematicians call this situation a function. Notice also that as the cos c increases, the sin c decreases. If we incline the ladder so that the base is 6. Comparing this result with example two we find that:. That is why we call the ratio of the adjacent and the hypotenuse the "co-sine" of the angle. Since the sine, cosine, and tangent are all functions of the angle c , we can determine measure the ratios once and produce tables of the values of the sine, cosine, and tangent for various values of c.

Later, if we know the value of an angle in a right triangle, the tables will tell us the ratio of the sides of the triangle. If we know the length of any one side, we can solve for the length of the other sides.

Or if we know the ratio of any two sides of a right triangle, we can find the value of the angle between the sides. We can use the tables to solve problems. Some examples of problems involving triangles and angles include the forces on an aircraft in flight, the application of torques , and the resolution of the components of a vector.

Here are tables of the sine, cosine, and tangent which you can use to solve problems. Activities: Guided Tours Navigation.. Beginner's Guide Home Page.