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Trigonometry Mind-Map

Applications of Trigonometry to Problem Solving

Ambiguous Case

Proof of the Law of Cosines

credit to:http://www.regentsprep.org/regents/math/algtrig/att12/derivelawofsines.htm

Triangle trigonometry can be applied in many real life situations. One important example can be in the use of navigation and bearing. Triangle trigonometry can be used in this situation to find bearings of one point to another using the distance between points and known angles.

Law of Cosines

When the only pieces information for a triangle given are two adjacent sides, and a non-included angle, it is possible for the non-identified side to swing inwards/outwards, creating an entirely different triangle; thus, an SSA (side-side-angle) triangle, as it were, could lead to a single triangle, two potential triangles, or the side lengths and angle given could result in an impossible triangle.

Graphs Of Trig Functions

A mathematical law which states that:

Each trigonometric graph follows this basic formula structure: y=a(function)[b(x+c)]+d

Law of Cosine

LAW OF SINES

The Law of Cosine states that c^2=(a^2)+(b^2)-2(a)(b)(cos(C))

Trig Ratio Values for any Angle

Figure 2

Area of a Triangle

Trig ratio values for any and all angles can be represented by the acronym: SYR CXR TYX.

Sin(§)θθ= Y/R or Opposite side/ Hypotenuse

Cos(§)=X/R or Adjacent side/ Hypotenuse

Tan(§)=Y/X or Opposite side/ Adjacent side

θ

or

The area would be acquired like so:

SEE FIGURE 2 FOR EXAMPLE

Unit Circle

Cosine Graph

Sine Graph

Tangent Graph

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