Trigonometry
Trigonometry
- from the Greek words trigonon (triangle) & metron (measure)
- the study of the relationships between angles and sides of a right triangle
What do we already know about angles and sides of right triangles?
- The sum of the angles of any triangle add up to 180°
- If one angle is 90° (definition of a right triangle), the other two angles are complementary.
- Special case triangles:
o Angle measurements: 30°-60°-90°
o Side ratios: [pic]
o Angle measurements: 45°-45°-90
o Side ratios: [pic]
We define the sides of a right triangle using three terms:
- Hypotenuse
o Across from the right angle
- Opposite
o Across from the angle in question
- Adjacent
o Next to the angle in question
The ratios between the sides of a right triangle are determined by the trigonometric functions:
|Basic trig function: |Sine (sinθ) |Cosine (cosθ) |Tangent (tanθ) |
| | | | |
| |opp |adj |opp |
| |hyp |hyp |adj |
|Reciprocal: |Cosecant (cscθ) |Secant (secθ) |Cotangent (cotθ) |
| | | | |
| |hyp |hyp |adj |
| |opp |adj |opp |
|Inverse: |arcsinθ |arccosθ |arctanθ |
|Inverse reciprocal: |arccscθ |arcsecθ |arccotθ |
I know the values for two sides of a right triangle. How do I find the third?
Pythagorean Theorem:
Plug in the values for the two known sides, and then solve.1
- The hypotenuse is ALWAYS the side denoted by c.
- The other two legs are a and b.
EXAMPLE
Find the values of the six trignometric functions associated with angle A.
1) Use the pythagorean theorem to find c.
2) Plug in the lengths of each side to define the six trig ratios
[pic]
Homework: P. 702 – 4, 5, 6, 15-18
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