Application of Sine, Cosine and Tangent

 

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

tri

The SineCosine and Tangent functions express the ratios of sides of a right triangle.

sine(angle)=opposite side / hypotenuse

Example 1:

tri

sin(∠L) = opposite / hypotenuse

sin(∠L) = 9 / 15

Example 2:

tri

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
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:

tri

cos(∠L) = adjacent / hypotenuse

cos(∠L) = 12 / 15

Example 2:

tri

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
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)

 

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