Questions and Answers
The cosine ratio is used to find missing angle measures and side measures in ______.
a right triangle
Based on the given triangle, what is the cosine of the 30 degree angle?
√³ / ₂
Based on the given triangle, what is the cosine of the 60 degree angle?
½
The sine of a 30 degree angle is equal to the cosine of a _____ degree angle.
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The cosine of an angle is a(n) _____.
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The cosine ratio is the _____ side over the hypotenuse.
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Find the measure of angle A.
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The legs of a right triangle are lengths x and x√3. What is the cosine of the smallest angle of the triangle?
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In a right triangle, the cosine of an acute angle is 1/2 and the hypotenuse measures 7 inches. What is the length of the side of the triangle adjacent to this angle?
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Find ∠A to the nearest degree. A ≈ ☐ degrees.
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If cos X = ⅘, then sin X = ______.
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If the cos of 22° = 0.9272, then the sin of ∠C = ______.
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In right ΔABC, ∠B is a right angle and sin ∠C = x. What is sin ∠A?
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In right △ABC, ∠B is a right angle and sin ∠C = x. What is cos ∠A?
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Find x to the nearest tenth.
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Which of the following expressions is equal to the value of x?
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Based on the diagram, which of the following represents the cosine of 70 degrees?
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Based on the diagram, all of the following are true except:
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Select all of the equations that represent a correct ratio between the angles and sides in right △ABC where ∠a has a measure of 40°.
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Study Notes
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.
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Test your knowledge of the cosine ratio in trigonometry with these interactive flashcards. Learn how it applies to right triangles and practice calculating the cosine for various angles. Perfect for students looking to reinforce their understanding of trigonometric concepts.
