math
7th Grade - Cosine

7th Grade lesson

10 - Cosine


The cosine is used to calculate engths or angles in a right-angled triangle. It is therefore necessary to have a right-angled triangle to be able to talk about the cosine and it must not be confused with the the adjacent edge and the hypotenuse. The hypotenuse is the name that is given to the largest side of a right-angled triangle. The adjacent edge is the edge that touches the angle in question but which is not the hypotenuse.
adjacent side and hypotenuse adjacent side and hypotenuse adjacent side and hypotenuse
The cosine of an angle is a number which is equal to the length of the adjacent edge divided by the length of the hypotenuse.

the cosine formula

cosine use
A=50°, AB=3cm, calculate AC.

calculation with the cosine
calculation with the cosine
calculation witht the cosine
calculation with the cosine
calculation with the cosinecm
using the cosine
PG=10cm, P=30°, calculate PS.

calculation with the cosine
calculation with the cosine
calculation with the cosine
calculation with the cosine
calculation with the cosinecm
using the cosine
PU = 2 cm, OU = 3 cm, calculate the angle U.

using the cosine of an angle
using the cosine
In order to find out the value fo the angle U, you must look for the cos-1 button on your calculationator and enter cos-1(2/3). The result will give the value of the angle U.

These three examples enable us to understand how to use the cosine formula. In order to find the calculation to be done during the last but one step in the first two examples, you must hide the lengths AC and PS and carry out a cross product with the remaining numbers.

In the second example, in order to calculate cos(30)×10, you must be careful not to enter cos(300) into the calculationator, 10×cos(30) is not the same as cos(300).

This is all that you need to know about the cosine. If you want a better understanding of what the cosine is, you can read the 9th Grade trigonometry lesson. Knowing how to use the cosine enables us to calculate many things, for example, if you have some time, try and calculate the height of the tree (you will need the cosine and pythagoras theorem).

problem on the application of the cosine

Jenny is 30 meters away from the tree, she measures 20° between the foot of the tree and the top of the tree, she would like to know the height of the tree.
If you wish, you can move on without solving this problem (the correction is not given). However, it is a good problem.


See also : trigonometry on fmaths.com



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The cosine

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