Flashcard Review 3.1 to 3.3

Front

What is the Law of Cosines?

Back

The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the relationship is given by: c² = a² + b² - 2ab * cos(C). This is useful for finding a side or angle in non-right triangles.

Front

How do you find the sine of an angle in a right triangle?

Back

In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1, meaning that for any angle θ, -1 ≤ sin(θ) ≤ 1.

Front

What is the definition of cotangent?

Back

Cotangent is the reciprocal of the tangent function. It is defined as: cot(θ) = cos(θ)/sin(θ) or cot(θ) = 1/tan(θ).

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180. For example, 180 degrees = 180 * (π/180) = π radians.

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in any triangle is always 180 degrees.

Front

What is the formula for finding the area of a triangle using sine?

Back

The area A of a triangle can be calculated using the formula: A = 1/2 * a * b * sin(C), where a and b are the lengths of two sides and C is the included angle.

Front

What is the significance of the terminal side of an angle?

Back

The terminal side of an angle is the position of the angle after it has been rotated from the initial side. It helps in determining the angle's position in the coordinate plane.

Front

How do you find the angle when given the sine value?

Back

To find the angle θ when given sin(θ) = k, use the inverse sine function: θ = sin⁻¹(k). Ensure to consider the correct quadrant for the angle.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².