Question

If sin theta = 144/145 then complete the following activity to find the cos theta​

Answer 1

$cos\theta=\dfrac{17}{145}$

Tips:

We know the relation between $sin\theta$ and $cos\theta$ as follows,

$sin^{2}\theta+cos^{2}\theta=1$

$\Rightarrow cos^{2}\theta=1-sin^{2}\theta$

$\Rightarrow \boxed{cos\theta=\sqrt{1-sin^{2}\theta}}$

Step-by-step explanation:

Given, $sin\theta=\dfrac{144}{145}$

Then, $cos\theta$

$=\sqrt{1-sin^{2}\theta}$

$=\sqrt{1-(\dfrac{144}{145})^{2}}$

$=\sqrt{1-\dfrac{20736}{21025}}$

$=\sqrt{\dfrac{21025-20736}{21025}}$

$=\sqrt{\dfrac{289}{21025}}$

$=\sqrt{\dfrac{17^{2}}{145^{2}}}$

$=\dfrac{17}{145}$

#SPJ3