To help you understand what the sine ratio is, we will do an activity that is similar to the one we did for tangent ratio.
In the lesson about tangent ratio, we used these triangles to find the tangent ratio.
Instead of doing ratios of opposite to adjacent, what if we did ratios of opposite to hypotenuse? Let us try that. To get the value of the hypotenuse, you have two choices.
You could use the pythagorean theorem or measure the lengths with a ruler.
I measured with a ruler and found the following lengths. Keep in mind that these measurements are not perfect and that is not the point.
Triangle on the left: 2.24 cm
Triangle in the middle: 3.8 cm
Triangle on the right: 5.3 cm
Notice that the ratio is closely equal to 0.71 cm no matter the size of the triangles.
There is a way to find a more accurate value for this ratio. Since the size of the triangle does not matter, you could use a value of 1 for the opposite and adjacent side.
Notice that this time, I am not using any unit. Again, it is because the size is irrelevant.
We use the pythagorean theorem this time to find the length of the hypotenuse
hypotenuse^{2} = 1^{2} + 1^{2}This trigonometric ratio is called sine ratio
Whenever the ratio is found by using the opposite side and the hypotenuse, we call it sine ratio instead of tangent ratio.
We then say that sine 45 degrees is equal to 0.707. In short, we can use the symbol sin instead of sine and write sin (45 degrees) = 0.707
When you do a ratio of adjacent to hypotenuse, this ratio is called the cosine ratio.
Take a look again at the triangles. You will see that the adjacent side has the same value as the opposite side.
This means that the cosine of 45 degrees is the same as the sine of 45 degrees.
You can use the symbol cos instead of cosine and write cos (45 degrees) = 0.707
Lesson #3: The unit circle
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.