Trigonometry - Cosine Ratio Flashcards

Cosine Ratio in Trigonometry

• The cosine ratio identifies relationships in right triangles to calculate missing angles and side lengths.
• The cosine of a 30-degree angle is represented as √³ / ₂.
• The cosine of a 60-degree angle is equal to ½.

Angle Relationships

• The sine of a 30-degree angle is equivalent to the cosine of a 60-degree angle.
• In a right triangle, if x represents the lengths of the legs, the cosine of the smallest angle is √³ / ₂.

Angle Measurement

• The measure of angle A in certain triangles can be calculated as 57 degrees.
• For a right triangle where the cosine of an acute angle equals 1/2 and the hypotenuse measures 7 inches, the adjacent side length is 3.5 inches.
• To find an unknown angle, consulting a trigonometric table may reveal that A is approximately 47 degrees.

Trigonometric Values

• If cos X equals ⅘ for an acute angle X, then sin X would be ⅗.
• In triangle ABC, with ∠CAD measuring 22° and a side segment of 15 cm, if cos 22° = 0.9272, then sin ∠C = 0.9272.

Trigonometric Function Relationships

• For right triangle ABC with ∠B as a right angle, if sin ∠C = x, then sin ∠A = √(1 - x²).
• For right triangle ABC with ∠B as a right angle, if sin ∠C = x, then cos ∠A = x.

Finding Lengths and Values

• In certain geometric diagrams, approximating the value of x to the nearest tenth might yield 1.4.
• An equivalent expression for x could be 0.9(sin 50).
• Cosine relationships can be visualized in diagrams, such as x/12.4 for cos 70°.

Validity of Trigonometric Statements

• When analyzing a triangle, it is important to verify statements, for example, evaluating if cos 52 = x/24 is true based on given diagrams.
• Understanding the ratios between angles and sides in a triangle, for example, h = 11/cos 50° and h = 11/sin 40°, helps in applying the cosine ratio correctly.