Fall 2024 Final

Front

What is the formula to find the height reached by a ladder leaning against a wall?

Back

Height = Ladder Length * sin(Angle with the ground)

Front

What is the value of csc(θ) if the terminal side of θ contains the point (x, y)?

Back

csc(θ) = \frac{r}{y}, where r = \sqrt{x^2 + y^2}

Front

How do you simplify the expression sin(x)cos^2(x) - sin(x)?

Back

Factor out sin(x): sin(x)(cos^2(x) - 1) = -sin^3(x)

Front

What is the amplitude and period of the function y = -3sin(\frac{5\pi}{4}x)?

Back

Amplitude = 3, Period = \frac{8}{5}

Front

How do you find a negative coterminal angle for an angle in radians?

Back

Subtract 2π from the angle until it is negative.

Front

What is the relationship between sine and cosine in a right triangle?

Back

sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse.

Front

What is the Pythagorean identity involving sine and cosine?

Back

sin^2(θ) + cos^2(θ) = 1.

Front

How do you convert degrees to radians?

Back

Multiply degrees by \frac{\pi}{180}.

Front

What is the formula for the period of a sine function?

Back

Period = \frac{2\pi}{b}, where b is the coefficient of x in sin(bx).

Front

What is the definition of cotangent?

Back

cot(θ) = \frac{1}{tan(θ)} = \frac{cos(θ)}{sin(θ)}.