Notes 7-4 Trigonometry. In Right Triangles: In any right triangle If we know Two side measures: We...

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Notes 7-4 Trigonometry

Transcript of Notes 7-4 Trigonometry. In Right Triangles: In any right triangle If we know Two side measures: We...

Page 1: 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.

Notes 7-4

Trigonometry

Page 2: 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.

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.

Page 3: 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.

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)

Page 4: 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.

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.

Page 5: 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.

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

Page 6: 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.
Page 7: 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.

SOHCAHTOA S→Sin O→Opposite H→Hypotenuse C→Cos A→Adjacent H→Hypotenuse T→Tan O→Opposite A→Adjacent

Page 8: 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.

Example: Finding Trigonometric Ratios

Write the trigonometric ratios as a fraction and as a decimal rounded to the nearest hundredth.

Page 9: 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.

Example:

Write the trigonometric ratios as a fraction and as a decimal rounded tothe nearest hundredth.


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