Cosine Theorem and Its Consequences

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What is the cosine theorem used for?
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The cosine theorem is used to calculate the lengths of sides or angles in triangles, especially when the triangle is not a right triangle.
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What is the formula for the cosine theorem?
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In a triangle with sides a, b, and c, and angle C opposite side c, the formula is: c² = a² + b² - 2ab * cos(C).
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How does the cosine theorem relate to the Pythagorean Theorem?
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When the angle is 90 degrees, the cosine of the angle is zero, and the cosine theorem simplifies to the Pythagorean Theorem: c² = a² + b².
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In what type of triangles can the cosine theorem be applied?
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The cosine theorem can be applied to any triangle, whether it is a right triangle, acute, or obtuse.
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What is another name for the cosine theorem?
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Another name for the cosine theorem is the Law of Cosines.
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How can the cosine theorem help in finding angles in a triangle?
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By rearranging the cosine theorem formula, you can solve for cos(C), and then use the inverse cosine function to find the angle C.
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What must you know to use the cosine theorem to find the length of a side?
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You must know the lengths of the other two sides and the measure of the angle between them.
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What does cos(C) represent in the cosine theorem formula?
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cos(C) represents the cosine of angle C, which is the angle opposite the side you are solving for.
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Can the cosine theorem be used to solve real-world problems?
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Yes, it can be used in navigation, engineering, and physics problems involving non-right triangles.
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What is a consequence of the cosine theorem when two sides and an included angle are known?
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A consequence is that you can find the length of the third side of the triangle.
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What is the inverse cosine function used for?
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It is used to determine the measure of an angle when the cosine of the angle is known.
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Why is the cosine theorem important in trigonometry?
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It allows you to solve for unknown sides or angles in triangles where other basic trigonometric identities do not apply.
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How does the cosine theorem help in determining triangle types?
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It helps deduce if a triangle is acute, obtuse or right-angled by comparing sides and using the angles derived from the theorem.
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What must you provide to calculate an angle using the cosine theorem?
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You must know the lengths of all three sides of the triangle.
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In mathematical problems, when would you prefer the cosine theorem over the sine theorem?
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You would prefer the cosine theorem when you have two sides and the included angle or all three sides and need to find an angle.
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