Week 17- Trig Summary

GENERALLY

Trigonometry definition:

trigonometry can be defined as simply as the mathematics involving the relationships between side lengths and angles of a triangle.

New vocabulary:

terminal arm: the line found within any of the 4 quadrants, creating an angle

coterminal angles: angles that share the same initial and terminal sides

quadrantal angles: angles that lie directly on the x and/or y axis (ie. 0°, 360°, 90°, 180°, 270°)

Rotational angle: the angle between 0° and the terminal arm

reference angle: the angle measured between the closest seperation of the x-axis and the terminal arm.

LESSONS SUMMARY

6.1 General updates-

Calculating the reference angle: ref angle= 180 – 92= 88°

calculating the coterminal angle:

hypotenus=radius

sides= x & y

$a^2+b^2=c^2$ ——> $x^2+y^2=r^2$

6.2 Exact Trig Values

sin=y/r, cos=x/r, tan=y/x

To remeber in which quadrants each ratio is positive: CAST rule

Special Triangles

originally a square:

originally an equilateral triangle:

The Sine Law

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

this formula can be modified so that the variable for which you are solving (either an angle or side) can be solved in fewer steps.

The Cosine Law

To be used if there are no angles with corresponding side lengths given and thus sine law will not work

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