Blanpied precal midterm 2024 b

Front

What is the formula to find the area of a triangle using SAS (Side-Angle-Side)?

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 the two sides and C is the included angle.

Front

How do you find the smallest angle in a triangle given the lengths of all three sides?

Back

Use the Law of Cosines: cos(C) = (a^2 + b^2 - c^2) / (2ab). Solve for angle C, and the smallest angle will be the one corresponding to the smallest side.

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1]. This means that the output of the sine function will always be between -1 and 1.

Front

What is the sine of 3π/2?

Back

The sine of 3π/2 is -1.

Front

What is the sine of 7π/6?

Back

The sine of 7π/6 is -1/2.

Front

What is the general solution for the equation sin(θ) = k?

Back

The general solutions are θ = arcsin(k) + 2nπ and θ = π - arcsin(k) + 2nπ, where n is any integer.

Front

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 its opposite angle is constant: (a/sin(A)) = (b/sin(B)) = (c/sin(C)).

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180.

Front

What is the value of sin(π/6)?

Back

The value of sin(π/6) is 1/2.

Front

What is the value of sin(π/3)?

Back

The value of sin(π/3) is √3/2.