Trigonometric Expressions and Identities Assessment

Factor the expression https://image.hypatiasys.com/images/362906ffb3239ca8e474cc47fdfd7a152a5980ba.png using the difference of squares formula:

• (\sin(x) + 2)(\sin(x) - 2)
• (\sin(x))(\sin(x) - 4)
• (\sin(x) + 1)(\sin(x) - 4)
• 2(\sin(x) - 2)

Simplify \(\frac{\sin(x)}{\cos(x)} + \frac{\cos(x)}{\sin(x)}\):

• \(\frac{\sin^2(x) + \cos^2(x)}{\sin(x)\cos(x)}\)
• \(\frac{\sin^2(x) + \cos^2(x)}{\tan(x)}\)
• \(\frac{1}{\sin(x)\cos(x)}\)
• \(\frac{2}{\sin(2x)}\)

What is the period of \(f(x) = 3\sin(2x)\)?

• \(\pi\)
• \(2\pi\)
• \(\frac{\pi}{2}\)
• \(4\pi\)

Simplify \(\sin^2(x) + \cos^2(x)\):

• \(\tan^2(x)\)
• \(2\)
• \(1\)
• \(0\)

What is the amplitude of \(y=4\cos(x)-2\)?

• \(1\)
• \(2\)
• \(4\)
• \(8\)

Express \(\tan(x)\) in terms of sine and cosine:

• \(\frac{\cos(x)}{\sin(x)}\)
• \(\frac{\sin(x)}{\cos(x)}\)
• \(\sin(x)\cos(x)\)
• \(\frac{1}{\sin(x)\cos(x)}\)

Factor \(\sin^2(x) + 2\sin(x) + 1\):

• (\sin(x) + 1)^2
• (\sin(x))(\sin(x) + 2)
• (\sin(x) - 1)(\sin(x) + 1)
• (\sin(x) + 1)(\sin(x) - 1)

Simplify \(\frac{1}{\csc(x)\sin\left(x\right)}\cdot\frac{1}{\cot\left(x\right)}\):

• \(\sec(x)\)
• \(\cos(x)\)
• \(\sin(x)\)
• \(\tan(x)\)

Solve \(\sin(x) = 0\) on \[0, 2\pi]:

• \(x = 0, \pi, 2\pi\)
• \(x = \frac{\pi}{2}, \frac{3\pi}{2}\)
• \(x = \pi\)
• \(x = 0, 2\pi\)

Express \(\cot(x)\) in terms of sine and cosine:

• \(\frac{\sin(x)}{\cos(x)}\)
• \(\frac{\cos(x)}{\sin(x)}\)
• \(\sin(x)\cos(x)\)
• \(\frac{1}{\sin(x)\cos(x)}\)