Pre-Calculus Trigonometry Review (Unit 3)

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What is the Law of Cosines?

Back

The Law of Cosines states that for any triangle with sides a, b, and c opposite to angles A, B, and C respectively, the following holds: c² = a² + b² - 2ab * cos(C). It is used to find unknown angles or sides in a triangle.

Front

How do you find the angle using the Law of Cosines?

Back

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

Front

What is cotangent (cotΘ)?

Back

Cotangent is the reciprocal of tangent. It is defined as cot(Θ) = adjacent / opposite in a right triangle. It can also be expressed as cot(Θ) = 1/tan(Θ).

Front

How do you calculate cotangent if you know sine and cosine?

Back

Cotangent can be calculated using cot(Θ) = cos(Θ) / sin(Θ). If you have the values of sine and cosine for an angle, you can find cotangent.

Front

What is the Law of Sines?

Back

The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). It is useful for solving triangles when you know some angles and sides.

Front

How do you use the Law of Sines to find a side?

Back

To find a side using the Law of Sines, rearrange the formula: a = (b * sin(A)) / sin(B). You need to know at least one side and its opposite angle.

Front

What is the inverse tangent function?

Back

The inverse tangent function, denoted as tan⁻¹ or arctan, is used to find an angle whose tangent is a given number. For example, if tan(Θ) = x, then Θ = tan⁻¹(x).

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Back

Front

What is the relationship between sine and cosine?

Back

The relationship between sine and cosine is given by the Pythagorean identity: sin²(Θ) + cos²(Θ) = 1. This means that for any angle, the square of the sine plus the square of the cosine equals one.

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1. This means that for any angle, the sine value will always fall within this interval.