Podcast
Questions and Answers
What is the value of $sin^2(2)$?
What is the value of $sin^2(2)$?
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?
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?
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?
Signup and view all the answers
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?
Signup and view all the answers
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: $\theta = \frac{180l}{\pi r}$
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of trigonometry equations and identities with this quiz covering topics such as sine, cosine, tangent, quadrants, and angle measures. Solve equations involving trigonometric functions and explore identities to find values of expressions.
