Sem I Final Practice

Front

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 formula is: c² = a² + b² - 2ab cos(C). It is used to find a side or angle in a triangle.

Front

How do you solve for an angle in a triangle?

Back

To solve for an angle in a triangle, you can use the Law of Cosines or the Law of Sines, depending on the information given. The Law of Cosines is particularly useful when you know the lengths of all three sides.

Front

What is the formula for converting radians to degrees?

Back

To convert radians to degrees, use the formula: degrees = radians × (180/π). For example, to convert 11π/6 radians to degrees, multiply by (180/π) to get 330 degrees.

Front

What is the inverse function of f(x)?

Back

The inverse function f⁻¹(x) swaps the input and output of the original function. If f(x) passes through points (a, b), then f⁻¹(x) will pass through (b, a).

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials. For example, f(x) = p(x)/q(x), where p(x) and q(x) are polynomials.

Front

What does the graph of f(x) = -8/(x+2) + 2 look like?

Back

The graph of this function is a hyperbola that approaches the vertical asymptote x = -2 and the horizontal asymptote y = 2.

Front

What is the significance of the vertex in a rational function?

Back

The vertex of a rational function is the point where the function changes direction. It is often the maximum or minimum point of the graph.

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts of a rational function, set the numerator equal to zero and solve for x. The x-intercepts are the points where the graph crosses the x-axis.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. This relationship is fundamental in trigonometry and is used in the Law of Sines and Law of Cosines.

Front

What is the purpose of the Law of Sines?

Back

The Law of Sines is used to find unknown angles or sides in a triangle when you know either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).