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:    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 Adjacent / Hypotenuse 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 to the nearest hundredth.