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Use $\\sin^{-1}$.

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Given $y=\\var{y1}, r=\\var{r1}$, find $\\theta$.

$\\theta=$ [[0]]

Use $\\cos^{-1}$.

Given $x=\\var{x2}, r=\\var{r2}$, find $\\theta$.

$\\theta=$ [[0]]

Use $\\tan^{-1}$.

Given $x=\\var{x3}, y=\\var{y3}$, find $\\theta$.

$\\theta=$ [[0]]

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The following parts refer to a right-angled triangle with hypotenuse length denoted by $r$ and horizontal and vertical side lengths denoted by $x$ and $y$. The angle $\\theta$ is as indicated in the diagram below. Each part gives two side lengths and you are asked to deduce the size of the angle $\\theta$ using appropriate inverse trigonometrical functions. Express your answers in radians, written as decimals to 3dp.

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Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.

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(a) $\\sin \\theta =\\dfrac{\\var{y1}}{\\var{r1}}$ so $\\theta= \\sin^{-1} \\left( \\dfrac{\\var{y1}}{\\var{r1}}\\right) = \\var{t1}$.

(b) $\\cos \\theta =\\dfrac{\\var{x2}}{\\var{r2}}$ so $\\theta= \\cos^{-1} \\left( \\dfrac{\\var{x2}}{\\var{r2}}\\right) = \\var{t2}$.

(c) $\\tan \\theta =\\dfrac{\\var{y3}}{\\var{x3}}$ so $\\theta= \\tan^{-1} \\left( \\dfrac{\\var{y3}}{\\var{x3}}\\right) = \\var{t3}$.

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