Lecture 22 Sean Nov 19

Front

What is the general solution for the equation \( \sin(x + \frac{\pi}{2}) = \frac{1}{2} \)?

Back

The general solutions are \( x = -\frac{\pi}{3} + n(2\pi) \) and \( x = \frac{\pi}{3} + n(2\pi) \), where \( n \) is any integer.

Front

What is the general solution for the equation \( \tan(x) = \sqrt{3} \)?

Back

The general solution is \( x = \frac{\pi}{3} + n\pi \), where \( n \) is any integer.

Front

How many solutions are there for the equation \( \sin(x) = \frac{\sqrt{2}}{2} \)?

Back

There are infinitely many solutions.

Front

What is the range of the sine function?

Back

The range of the sine function is \([-1, 1]\).

Front

What is the period of the sine function?

Back

The period of the sine function is \(2\pi\).

Front

What is the period of the tangent function?

Back

The period of the tangent function is \(\pi\).

Front

What is the value of \( \sin(\frac{\pi}{6}) \)?

Back

The value of \( \sin(\frac{\pi}{6}) \) is \(\frac{1}{2}\).

Front

What is the value of \( \tan(\frac{\pi}{3}) \)?

Back

The value of \( \tan(\frac{\pi}{3}) \) is \(\sqrt{3}\).

Front

What is the general solution for \( \sin(x) = k \) where \( k \) is in the range of the sine function?

Back

The general solution is \( x = \arcsin(k) + n(2\pi) \) and \( x = \pi - \arcsin(k) + n(2\pi) \), where \( n \) is any integer.

Front

What is the general solution for \( \cos(x) = k \) where \( k \) is in the range of the cosine function?

Back

The general solution is \( x = \arccos(k) + n(2\pi) \) and \( x = -\arccos(k) + n(2\pi) \), where \( n \) is any integer.