PCCP Practice Midterm Exam

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It is expressed as: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is useful for finding a side or angle when you have two sides and the included angle or all three sides. It is expressed as: \( c^2 = a^2 + b^2 - 2ab \cos(C) \)

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by \( \frac{\pi}{180} \). For example, to convert 180 degrees to radians: \( 180 \times \frac{\pi}{180} = \pi \) radians.

Front

What is the range of values for \( \theta \) in trigonometric equations?

Back

The range of values for \( \theta \) in trigonometric equations is often specified as \( 0 \leq \theta < 2\pi \) for angles measured in radians.

Front

What is the cosine function?

Back

The cosine function, denoted as \( \cos(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the adjacent side to the hypotenuse in a right triangle.

Front

What is the sine function?

Back

The sine function, denoted as \( \sin(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the opposite side to the hypotenuse in a right triangle.

Front

What does it mean to solve for all values of \( \theta \)?

Back

Solving for all values of \( \theta \) means finding all angles that satisfy the given trigonometric equation within the specified range, typically \( 0 \leq \theta < 2\pi \).

Front

What is the cosecant function?

Back

The cosecant function, denoted as \( \csc(\theta) \), is the reciprocal of the sine function. It is defined as: \( \csc(\theta) = \frac{1}{\sin(\theta)} \).

Front

What is the significance of the angle in a triangle?

Back

The angles in a triangle determine the shape and size of the triangle. The sum of the interior angles of a triangle is always \( 180 \) degrees or \( \pi \) radians.

Front

How do you determine the number of possible triangles from given measurements?

Back

To determine the number of possible triangles, use the triangle inequality theorem and the given measurements. Analyze if the conditions allow for one, two, or no triangles to be formed.