3rd 6-Weeks Test Review

Front

What is the ground speed of an object moving at a constant speed of 100 mph heading N 45 E with a wind blowing 500 mph south?

Back

The ground speed is 435.1 mph.

Front

What is the equation for a sinusoidal function that has a vertical shift of 6 and an amplitude of 6?

Back

The equation is r = 6 + 6 sin θ.

Front

Convert the polar point (4, -\frac{3\pi}{2}) to rectangular coordinates.

Back

The rectangular coordinates are (0, 4).

Front

Solve the equation -2 + cot(θ) = -3 for 0 ≤ θ < 2π.

Back

The solutions are θ = \frac{3\pi}{4}, \frac{7\pi}{4}.

Front

What is the direction of the resultant vector for an airplane on a course bearing of 105° at 400 mph with a wind blowing 35 mph due east?

Back

The direction of the resultant vector is S76.2°E.

Front

Define ground speed in the context of vector addition.

Back

Ground speed is the speed of an object relative to the ground, calculated by combining its speed and direction with the wind speed and direction.

Front

What is the formula for converting polar coordinates (r, θ) to rectangular coordinates (x, y)?

Back

The formulas are x = r * cos(θ) and y = r * sin(θ).

Front

What is the amplitude of the function r = 6 + 6 sin θ?

Back

The amplitude is 6.

Front

How do you find the resultant vector when two vectors are involved?

Back

Use vector addition, which involves adding the components of the vectors in the x and y directions.

Front

What is the significance of the angle in polar coordinates?

Back

The angle θ in polar coordinates determines the direction of the point from the origin.