How do you find the exact values of $cos θ$ $costheta$ and $sin θ$ $sintheta$ when $tan θ = \frac{5}{12}$ $tantheta=5/12$ ?

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How do you find the exact values of $cos θ$ $costheta$ and $sin θ$ $sintheta$ when $tan θ = \frac{5}{12}$ $tantheta=5/12$ ?

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Answer 1 · 2016-11-07T18:10:28

sinθ= $\frac{5}{13}$ $5/13$

and cosθ= $\frac{12}{13}$ $12/13$

Explanation:

Draw a right triangle with base 12 and height 5 units with angle $θ$ $theta$ sitting on the base as shown below
enter image source here

Apply Pythagoras theorem to get hypotenuse= 13 units

Work out sin $θ = \frac{5}{13}$ $theta= 5/13$

and cos $θ = \frac{12}{13}$ $theta= 12/13$

Answer 2 · 2016-11-07T18:13:48

$cos θ = \frac{12}{13}$ $costheta=12/13$ and $sin θ = \frac{5}{13}$ $sin theta=5/13$

Explanation:

If $tan θ = \frac{5}{12} = \frac{o p p o s i t e s i d e}{a d j a c e n t s i d e}$ $tantheta=5/12= (opposite side)/(adjacent side)$
So the hypotenuse $= \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13$ $=sqrt(5^2+12^2)=sqrt169=13$
$cos θ =$ $costheta=$ (adjacent side)/(hypotenuse) $= \frac{12}{13}$ $=12/13$
$sin θ =$ $sintheta=$ (opposite side)/(hypotenuse) $= \frac{5}{13}$ $=5/13$

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How do you find the exact values of $cos θ$ $costheta$ and $sin θ$ $sintheta$ when $tan θ = \frac{5}{12}$ $tantheta=5/12$ ?

2 Answers

Explanation:

Explanation:

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How do you find the exact values of $cos θ$ $costheta$ and $sin θ$ $sintheta$ when $tan θ = \frac{5}{12}$ $tantheta=5/12$ ?