Sine (Sin), Cosine (Cos), Tangent (Tan)
How to remember the sides of a triangle:
How to remember the sides of a triangle:
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| This is called "beta" |
Simple, the angle with the beta symbol, represents the viewpoint.
The opposite side will always face right across from the angle "beta".
The hypotenuse will always be across from the 90°.
The adjacent side will always be right below the hypotenuse; the line between the angle "beta" and 90°.
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| Diagram for Reference |
Awesome! Now we can learn the Sin, Cos, and Tan formulas! They make life a bit more easier.
Naming each makes it easier to remember:
Soh for Sin because Sin= Opposite/Hypotenuse
Cah for Cos because Cos= Adjacent/Hypotenuse
and Toa for Tan because Tan= Opposite/Adjacent
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| For reference purposes |
Ex.1
o = 5, h = 10 find beta.
Press "2nd" button on calculator.
Following, press the "SIN" button
Next, enter the value of your opposite side. In this case, 5.
Then press the division sign. This makes a ratio
Lastly, enter the value of your hypotenuse side. In this case, 10.
Your result should be "Sin of 'beta' = 30°."
Ex.2 Only beta and one side are given
o = 1, "beta"= 90° find hypotenuse.
This is better written and understood as Sin 90° = 1/h, otherwise "1/Sin 90° = h/1"
Cross multiplication.
Start by entering your opposite value. In this case 1.
Then press the division sign
Press the "SIN" button.
Enter the value of "beta". In this case 90.
Your result should be h = 1.
Cos is used for right triangles that relate to the values of adjacent side and hypotenuse to find the value of the triangle's "beta" angle.
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| For reference purposes |
Ex.1
a = 5, h = 10 find beta.
Press "2nd" button on calculator.
Following, press the "COS" button
Next, enter the value of your adjacent side. In this case, 5.
Then press the division sign. This makes a ratio
Lastly, enter the value of your hypotenuse side. In this case, 10.
Your result should be "Cos of 'beta' = 60°."
Ex.2 Only beta and one side are given
a = 4, "beta"= 60° find hypotenuse.
This is better written and understood as Cos 60° = 4/h, otherwise "4/Cos 60° = h/1"
Cross multiplication.
Start by entering your adjacent value. In this case 4.
Then press the division sign
Press the "COS" button.
Enter the value of "beta". In this case 60.
Your result should be h = 8.
Tan is used for right triangles that relate to the values of opposite side and adjacent side to find the value of the triangle's "beta" angle.
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| For reference purposes |
Ex. 1
o = 10, a = 10 find beta.
Press "2nd" button on calculator.
Following, press the "TAN" button
Next, enter the value of your opposite side. In this case, 10.
Then press the division sign. This makes a ratio
Lastly, enter the value of your adjacent side. In this case, 10.
Your result should be "Tan of 'beta' = 45
Ex.2 Only beta and one side are given
o = 10, "beta"= 45° find adjacent side.
This is better written and understood as Tan 45° = 10/a, otherwise "10/Tan 45° = h/1"
Cross multiplication.
Start by entering your adjacent value. In this case 10.
Then press the division sign
Press the "TAN" button.
Enter the value of "beta". In this case 45.
Your result should be a = 10.
