Trigonometry can be described as the relation of the elements of side and angles in a 90 degree triangle. This can be also named as the right angle triangle.

The sides of the Right Angle Triangle

The right angle triangle has three sides all with different lengths.

The longest one is the hypotenuse. The others are the opposite and the adjacent.

How do we differentiate between the opposite and the adjacent?

Well, this depends on the type of question asked and the angle which is used( this angle is not a right angle).

Now the ''opposite'' is the angle which is opposite to the angle asked or shown in the question. the longest side is the hypotenuse and the other one is the adjacent.

Look at the diagram for a better understanding. (The angle involved doesn't have to be in the same place)

Further explanation will be made as we progress

Trigonometry has three functions.

• sine
• cosine
• tangent

All of the functions mentioned above are related into each other. While using each sign, the question will give you two sides and one angle. One of them will be unknown and you'll have to find them using the signs you have.

I'll explain each one alone. But for now remember this phrase ''SOHCAHTOA''.

• SOH is for sine opposite hypotenuse ( we use sine when we have the opposite and hypotenuse involved)
• CAH is for cosine adjacent hypotenuse ( we use cosine when adjacent and hypotenuse involved)
• TOA is for tangent opposite adjacent. ( use tangent when there is opposite and adjacent involved)

In this page I'll only write about the tangent and its inverse. The others I'll talk separately.

The tan function is the ratio of the length of the opposite side of the right angle triangle to the length of the adjacent.

How do we use it?

For a triangle with an unknown side. (Diagram tan)

Here, they give you one side and one angle and you'll have to find the unknown side. Look at diagram (tan)

Here the question states that the angle is 36, the opposite is 7cm. You have to find the adjacent (X).

Answer:

1. SOHCAHTOA, we have to use tangent since we have the opposite and adjacent involved.
2. tan36= opposite/adjacent→ tan36=7/x
3. switch tan36 into a number using your calculator. enter 36 into your calculator and press tan as shown.(In some calculators you have to press tan then the number.)you will get 0.7265(estimation)
4. so 0.7265=7/x→ cross multiply 0.7265x=7
5. divide each side by 0.7265→ 0.7265x/0.7265=7/0.7265
6. x=9.64 (3 s.f)

For a triangle with an unknown angle( we name it theta (θ). (Diagram tan-1)

In this type of question we don't have the angles, but we do have the sides. so now what we will do is the following.

1. list what we know. opposite 7cm, adjacent 9cm, angle unknown(we have to find)
2. SOHCAHTOA→ we choose toa again
3. write the equation→ tanθ= opposite/adjacent (remember θ is the sign for the unknown angle)
4. switch what you know into numbers, in this case the opposite and adjacent.→ tanθ=7/9→tanθ=0.778(estimation)
5. since we have to find the angle, we have to inverse the equation. to do this, enter 0.778, press ''shift'' on your calculator and then press tan. this will give you tan inverse (tan^-1)
6. this will give you 37.9 (3 s.f). this is your angle

Well that is only one of the functions.

I wrote about the cosine function separately .

http://hubpages.com/t/b4cea

I hope ı was able to help.

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