Back to: MATHEMATICS SS1
Welcome to class!
In today’s class, we will be talking about the application of sine, cosine and tangent. Enjoy the class!
Application of Sine, Cosine and Tangent
The Sine, Cosine and Tangent functions express the ratios of sides of a right triangle.
sine(angle)=opposite side / hypotenuse
Example 1:
sin(∠L) = opposite / hypotenuse
sin(∠L) = 9 / 15
Example 2:
sin(∠K) = opposite / hypotenuse
sin(∠K) = 12 / 15
Range of values of sine
For those comfortable in “Math Speak”, the domain and range of Sine are as follows.
- The domain of Sine = all real numbers
- Range of Sine = {-1 ≤ y ≤ 1}
The sine of an angle has a range of values from -1 to 1 inclusive. Below is a table of values illustrating some key sine values that span the entire range of values.
| Angle | Sine of the Angle |
| 270° | Sin (270°) = -1 (smallest value that sine can have) |
| 330° | Sin (330°) = -½ |
| 0° | Sin (0°) = 0 |
| 30° | Sin (30°) = ½ |
| 90° | Sin (90°) = 1 (greatest value that sine can have) |
The cosine ratio
The cosine of an angle is always the ratio of the (adjacent side/ hypotenuse).
cosine(angle)=adjacent side / hypotenuse
Example 1:
cos(∠L) = adjacent / hypotenuse
cos(∠L) = 12 / 15
Example 2:
cos(∠K) = adjacent / hypotenuse
cos(∠K) = 9 / 15
Range of values of cosine
For those comfortable in “Math Speak”, the domain and range of cosine are as follows.
- Domain of Cosine = all real numbers
- Range of Cosine = {-1 ≤ y ≤ 1}
The cosine of an angle has a range of values from -1 to 1 inclusive. Below is a table of values illustrating some key cosine values that span the entire range of values.
| Angle | Cosine of the angle |
| 0° | Cos (0°) = 1 (greatest value that cosine can ever have) |
| 60° | Cos (60°) =½ |
| 90° | Cos (90°) = 0 |
| 120° | Cos (120°) = -½ |
| 180° | Cos (180°) = -1 (smallest value that cosine can ever have) |
We hope you enjoyed the class.
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