The terminal side of $θ$ $theta$ in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of $θ$ $theta$ ?

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The terminal side of $θ$ $theta$ in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of $θ$ $theta$ ?

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Answer 1 · 2018-06-19T08:19:32

See explanation.

Explanation:

If you have a point ion the terminal side $(x, y)$ $(x,y)$ then you have to calculate the didtance between the point and the origin

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

$r = \sqrt{0^{2} + 3^{2}} = 3$ $r=sqrt(0^2+3^2)=3$

Now the trig functions are defined as:

$sin θ = \frac{y}{r}$ $sin theta=y/r$

$sin θ = \frac{0}{3} = 0$ $sin theta=0/3=0$

$cos θ = \frac{x}{r}$ $cos theta=x/r$

$cos θ = \frac{3}{3} = 1$ $cos theta=3/3=1$

$tan θ = \frac{y}{x}$ $tan theta=y/x$

$tan θ = \frac{0}{3}$ $tan theta=0/3$

$cot θ = \frac{x}{y}$ $cot theta=x/y$

$cot θ = \frac{3}{0}$ $cot theta=3/0$ $cot θ$ $cot theta$ is undefined.

$sec θ = \frac{r}{x}$ $sec theta=r/x$

$sec θ = \frac{3}{3} = 1$ $sec theta=3/3=1$

$csc θ = \frac{r}{y}$ $csc theta=r/y$

$csc θ = \frac{3}{0}$ $csc theta=3/0$ ** $csc θ$ $csc theta$ is undefined **

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The terminal side of $θ$ $theta$ in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of $θ$ $theta$ ?

1 Answer

Explanation:

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

$sin θ = \frac{y}{r}$ $sin theta=y/r$

$cos θ = \frac{x}{r}$ $cos theta=x/r$

$tan θ = \frac{y}{x}$ $tan theta=y/x$

$cot θ = \frac{x}{y}$ $cot theta=x/y$

$sec θ = \frac{r}{x}$ $sec theta=r/x$

$csc θ = \frac{r}{y}$ $csc theta=r/y$

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The terminal side of θtheta in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of θtheta?

1 Answer

Explanation:

r=√x2+y2r=sqrt(x^2+y^2)

sinθ=yrsin theta=y/r

cosθ=xrcos theta=x/r

tanθ=yxtan theta=y/x

cotθ=xycot theta=x/y

secθ=rxsec theta=r/x

cscθ=rycsc theta=r/y

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Impact of this question

The terminal side of $θ$ $theta$ in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of $θ$ $theta$ ?

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

$sin θ = \frac{y}{r}$ $sin theta=y/r$

$cos θ = \frac{x}{r}$ $cos theta=x/r$

$tan θ = \frac{y}{x}$ $tan theta=y/x$

$cot θ = \frac{x}{y}$ $cot theta=x/y$

$sec θ = \frac{r}{x}$ $sec theta=r/x$

$csc θ = \frac{r}{y}$ $csc theta=r/y$