The Sine Function

The Sine function is a formula that you can use to solve for a right triangle's side lengths. Sine is abbreviated as SIN.

sin formula The sin formula contains three variables: Ɵ theta, opposite, and hypotenuse. All three variables are given to you as part of the problem. Typically one variable will be missing and we can use the equation to calcuate it.

The two images below show the correct labeling of opp, adj, and hypotenuse in our triangles. Labeling a triangle wrong will result in the wrong answer, The location of the angle symbol theta is the main characteristic you must pay attention to when labeling.

shading1 shading2

Example 1: Calculate the length of the hypotenuse. ex1

Example 2: Calculate the length of the hypotenuse. ex2
Example 3: Calculate the length of the hypotenuse. ex3
Example 4: Calculate the length of the opposite side. ex4
Example 5: Calculate the length of the opposite side. ex5

To utilize the sine function, it is important to label the opposite, adjacent, and hypotenuse correctly. With practice all things will become perfect! It is also important that you master using the three trig functions: sin, cos, and tan. They will be a part of Algebra 2, Pre-Calculus, and beyond. Trig is hard to learn at first but once you get it it is really fun! Trigonometry was the topic I liked to teach the most because it is so rewarding once you understand it.

Let's try a few practice problems:
Example 1:
pract 1

Example 2:
pract 2

Example 3:
pract 3