Graphs Of Trigonometric Functions Assessment Test

Explanation
There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. These functions are commonly used in mathematics and physics to relate the angles of a right triangle to the lengths of its sides. Each function has a specific relationship with the angles and sides, allowing for calculations and solving various trigonometric equations.

Explanation
The cosine rule can be used to find the length of a side or the size of an angle in a triangle. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them. Therefore, by rearranging the formula, we can solve for the length of a side or the size of an angle in a triangle using the cosine rule.

Explanation
The reciprocal of cosine is secant. This is because secant is defined as the reciprocal of cosine, meaning that if we take the multiplicative inverse of cosine, we get secant. In other words, if we divide 1 by cosine, we obtain secant. Therefore, secant is the correct answer.

Explanation
The cosine graph is a periodic function that oscillates between 1 and -1. The value of 0 occurs at the x-intercepts of the graph, which are evenly spaced along the x-axis. At these points, the graph touches the x-axis but does not cross it, creating a horizontal line. This type of line is called an asymptote, as it represents a value that the function approaches but never reaches. Therefore, any place on the cosine graph where the value is 0 creates an asymptote.

Explanation
Any fraction with 0 in the denominator is undefined. This is because division by zero is not defined in mathematics. When the denominator of a fraction is zero, it means that the fraction cannot be evaluated and does not have a meaningful value. Therefore, the correct answer is undefined.

Explanation
The correct answer is "Sinusoidal wave" because a cosine curve is a type of sinusoidal wave. A sinusoidal wave is a wave that has the same shape as a sine or cosine function, which is a smooth, periodic oscillation. The cosine function specifically represents the x-coordinate of a point on the unit circle as it rotates counterclockwise. Therefore, the cosine curve on the graph is in the shape of a sinusoidal wave.

Explanation
The cosecant of an angle in a right triangle is equal to the length of the hypotenuse divided by the length of the opposite side. In this question, the length of the hypotenuse divided by the length of the opposite side is the cosecant.

Explanation
The set of all points in the plane of the form (x, f(x)) represents the graph of a function. In a graph of a function, each value of x corresponds to a unique value of f(x), meaning that for every x-coordinate, there is only one y-coordinate. This distinguishes it from other options such as "Function trig" or "Trig," which do not specify the uniqueness of the y-coordinate for each x-coordinate. "Coordinates" is a general term that can refer to any set of points in a plane, whereas "Graph of a function" specifically describes the relationship between x and f(x) in the given set of points.

Explanation
The product of the length of the opposite side and the length of the adjacent side is equal to the tangent of the angle. This relationship is derived from the trigonometric function called tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. Therefore, the correct answer is "Tangent of the angle."

Explanation
The product of the length of the opposite side and the length of the hypotenuse is the sine of a graph. This is because in a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, the product of these two lengths represents the sine of the angle in the graph.