5-9c61-4533-8ad8-f78987a7d994","topicSlug":"trigonometry-5","cards":[{"id":"cd8ac08b-2088-4217-b912-df1511f31eb0","cardType":"basic","front":"

What radian angle is one complete revolution?

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$2\\pi$ radians

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For a unit-circle point $(x,y)$ at angle $\\theta$, what does $x$ represent?

","back":"

$x=\\cos\\theta$

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For a unit-circle point $(x,y)$ at angle $\\theta$, what does $y$ represent?

","back":"

$y=\\sin\\theta$

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Provided $\\cos\\theta\\neq0$, $\\text{[...]}$.

","back":"

Provided $\\cos\\theta\\neq0$, $\\boxed{\\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta}}$.

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What is the range of $\\sin x$?

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$-1\\leq\\sin x\\leq1$

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At which values of $x$ is $\\sin x=0$?

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$x=n\\pi$, where $n$ is an integer.

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The period of $\\sin x$ and $\\cos x$ is $\\text{[...]}$.

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The period of $\\sin x$ and $\\cos x$ is $\\boxed{2\\pi}$.

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At which values of $x$ is $\\cos x=0$?

","back":"

$x=\\frac{\\pi}{2}+n\\pi$, where $n$ is an integer.

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How is the cosine graph obtained from the sine graph?

","back":"

Shift it $\\frac{\\pi}{2}$ units left.

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The phase-shift identity is $\\text{[...]}$.

","back":"

The phase-shift identity is $\\boxed{\\cos x=\\sin\\left(x+\\frac{\\pi}{2}\\right)}$.

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Why is $\\tan x$ undefined when $x=\\frac{\\pi}{2}+n\\pi$?

","back":"

Because $\\cos x=0$, causing division by zero.

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Where are the vertical asymptotes of $y=\\tan x$?

","back":"

$x=\\frac{\\pi}{2}+n\\pi$, where $n$ is an integer.

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The tangent function repeats according to $\\text{[...]}$.

","back":"

The tangent function repeats according to $\\boxed{\\tan(x+\\pi)=\\tan x}$.

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Why does tangent repeat after $\\pi$?

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Sine and cosine both change sign, so their ratio is unchanged.

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What symmetry does the cosine graph have?

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Reflection symmetry about the vertical axis.

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Cosine is even, so $\\text{[...]}$.

","back":"

Cosine is even, so $\\boxed{\\cos(-x)=\\cos x}$.

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How does odd symmetry simplify $\\sin(-x)$?

","back":"

$\\sin(-x)=-\\sin x$

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1.4.4 Trigonometry Flashcards

1.4.4 Trigonometry Flashcards