MATH 4 - Final Exam Review #9

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What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in the triangle. Formula: a/sin(A) = b/sin(B) = c/sin(C).

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What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to find a side or angle in a triangle when the Law of Sines cannot be applied. Formula: c² = a² + b² - 2ab*cos(C).

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How do you find the distance to an object using angles of elevation?

Back

To find the distance to an object using angles of elevation, you can use trigonometric ratios (like tangent) or the Law of Sines, depending on the information given.

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What is the formula for tangent in a right triangle?

Back

Tangent (tan) is defined as the ratio of the opposite side to the adjacent side. Formula: tan(θ) = opposite/adjacent.

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What is the formula for secant in trigonometry?

Back

Secant (sec) is the reciprocal of cosine. Formula: sec(θ) = 1/cos(θ).

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What is the formula for cosecant in trigonometry?

Back

Cosecant (csc) is the reciprocal of sine. Formula: csc(θ) = 1/sin(θ).

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What is the formula for cotangent in trigonometry?

Back

Cotangent (cot) is the reciprocal of tangent. Formula: cot(θ) = 1/tan(θ) = adjacent/opposite.

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How do you solve for an angle using the Law of Cosines?

Back

To solve for an angle using the Law of Cosines, rearrange the formula to isolate the cosine of the angle. For example, to find angle C: cos(C) = (a² + b² - c²) / (2ab).

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What is the relationship between angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the side opposite that angle. This is a key principle in both the Law of Sines and the Law of Cosines.

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What is the angle of elevation?

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal line.