Unit 9: Trigonometry

Key words

• RadianKey word · Unit 9RadianAn angle measured by comparing arc length with radius.Exactly: One radian subtends an arc equal in length to the radius. In general, $\theta =\frac{s}{r}$, where $s$ is arc length and $r>0$ is radius.Mix-up alert: Use radians in $s=r\theta$. Convert a degree measure before using this formula.See this in Key wordsClose meaning
• Unit circleKey word · Unit 9Unit circleA circle of radius one centered at the origin.Exactly: The points $(x,y)$ satisfying $x^2+y^2=1$. At angle $\theta$, the point is $(\cos \theta ,\sin \theta )$.Mix-up alert: Cosine is the horizontal coordinate; sine is the vertical coordinate.See this in Key wordsClose meaning
• Trigonometric ratioKey word · Unit 9Trigonometric ratioA comparison of side lengths in a right triangle.Exactly: For an acute angle in a right triangle, label opposite length $o$, adjacent length $a$, and hypotenuse $h$. Then $\sin \theta =\frac{o}{h}$, $\cos \theta =\frac{a}{h}$, and $\tan \theta =\frac{o}{a}$.Mix-up alert: Opposite and adjacent depend on which acute angle you chose.See this in Key wordsClose meaning
• IdentityKey word · Unit 9IdentityAn equation that works for every allowed input.Exactly: An equality true for every value in the common domain of its two sides.Mix-up alert: Checking one angle can disprove an identity but cannot prove it.See this in Key wordsClose meaning
• Trigonometric equationKey word · Unit 9Trigonometric equationAn equation with trigonometric expressions whose allowed solutions you must find.Exactly: An equality involving trigonometric functions, solved on a stated interval or as a general solution.Mix-up alert: Dividing by a factor can lose solutions where that factor is zero.See this in Key wordsClose meaning