Notes 7-4 Trigonometry. In Right Triangles: In any right triangle If we know Two side measures: We...
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Transcript of Notes 7-4 Trigonometry. In Right Triangles: In any right triangle If we know Two side measures: We...
Notes 7-4
Trigonometry
In Right Triangles:
In any right triangle If we know Two side measures: We can find third side measure. Using Pythagorean Theorem.
Special Right Triangles: 45-45-90 30-60-90 We only need to know one side measure to find other
side measures.
Trigonometry:
The study of triangle measures. Uses the relationships between sides and angle
measures. Trigonometric Ratio- Ratio of the lengths of the
sides of a right triangle. Three most common trigonometric ratios:
Sine (Sin) Cosine (Cos) Tangent (Tan)
A trigonometric ratio is a ratio of two sides of a right triangle.
Since these triangles are similar, their ratios of corresponding sides are equal.
Given a Right Triangle:
Sine of < A → Sin A = BC/AB
Sine of < B → Sin B = AC/AB
Cosine of < A → Cos A = AC/AB
Cosine of < B → Cos B = BC/AB
Tangent of < A → Tan A = BC/AC
Tangent of < B → Tan B = AC/BC
A
B
C
∆ABC
Opposite / Hypotenuse
Opposite / Hypotenuse
Adjacent / Hypotenuse
Adjacent / Hypotenuse
Opposite / Adjacent
Opposite / Adjacent
SOHCAHTOA S→Sin O→Opposite H→Hypotenuse C→Cos A→Adjacent H→Hypotenuse T→Tan O→Opposite A→Adjacent
Example: Finding Trigonometric Ratios
Write the trigonometric ratios as a fraction and as a decimal rounded to the nearest hundredth.
Example:
Write the trigonometric ratios as a fraction and as a decimal rounded tothe nearest hundredth.