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Questions and Answers
What is the value of $sin^2(2)$?
What is the value of $sin^2(2)$?
- $2$
- $1$ (correct)
- $4$
- $3$
If $tan(6x) = 2$, what is $sin(3x) + sin(2x) - sin(x)$ equal to?
If $tan(6x) = 2$, what is $sin(3x) + sin(2x) - sin(x)$ equal to?
- $7 sin(x) cos(x)$ (correct)
- $3 sin(x) cos(x)$
- $4 sin(x) cos(x)$
- $2 sin(x)$
If $cos(x) = x$ in quadrant III, what is the degree measure of angle x?
If $cos(x) = x$ in quadrant III, what is the degree measure of angle x?
- $120$ (correct)
- $60$
- $90$
- $30$
What does $(cos(x)+cos(y))^2 + (sin(x)-sin(y))^2$ simplify to?
What does $(cos(x)+cos(y))^2 + (sin(x)-sin(y))^2$ simplify to?
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If in a circle of radius $r$, an arc of length $l$ subtends an angle of $0$ radians, what is the formula for the radian measure?
If in a circle of radius $r$, an arc of length $l$ subtends an angle of $0$ radians, what is the formula for the radian measure?
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Study Notes
Trigonometric Identities
- $(\cos x + \cos y)^2 + (\sin x - \sin y)^2 = 4 \cos^2\left(\frac{x-y}{2}\right)$
- $(\cos x - \cos y) + (\sin x - \sin y) = 4 \sin^2\left(\frac{x-y}{2}\right)$
Sine Formulae
- $\sin x + \sin 3x + \sin 5x + \sin 7x = 4 \sin x \cos 2x \sin 4x$
- $(\sin 7x + \sin 5x) + (\sin 9x + \sin 3x) = (\cos 7x + \cos 5x) + (\cos 9x + \cos 3x)$
Trigonometric Relationships
- $\tan x = \frac{\sin x}{\cos x}$
- $\sin 3x + \sin 2x - \sin x = 4 \sin x \cos x \cos 3x$
- $\tan 3x = \tan(2x + x)$
Quadrant Angles
- Angle $x$ in Quadrant II: $\sin x = \frac{1}{2}, \tan x = -\sqrt{3}$
- Angle $x$ in Quadrant III: $\cos x = -\frac{1}{2}, \tan x = \sqrt{3}$
Radian Measure
- In a circle of radius $r$, an arc of length $l$ subtends an angle of $\theta$ radians: $l = r \theta$
- Radian measure: $\theta = \frac{l}{r}$
- Degree measure: $\theta = \frac{180l}{\pi r}$
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