The value of Cos (-Ф)
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Step-by-step explanation:
Given Trigonometric function as :
sin( - Ф ) = ![\frac{- 3}{5}](/tpl/images/0415/6562/5269a.png)
- sin Ф = ![\frac{- 3}{5}](/tpl/images/0415/6562/5269a.png)
So, sin Ф = ![\frac{ 3}{5}](/tpl/images/0415/6562/083de.png)
Now, as sin Ф = ![\dfrac{\textrm perpendicular}{\textrm hypotenuse}](/tpl/images/0415/6562/3ca1a.png)
So ,
= ![\frac{ 3}{5}](/tpl/images/0415/6562/083de.png)
So, perpendicular = 3
And hypotenuse = 5
Now, From Pythagoras Theorem
Base ² = Hypotenuse² - Perpendicular²
Or, Base ² = 5² - 3²
Or, Base ² = 25 - 9
Or, Base ² = 16
∴ Base = ![\sqrt{16}](/tpl/images/0415/6562/88b64.png)
I.e Base = 4
Now, Cos Ф = ![\dfrac{\textrm base}{\textrm hypotenuse}](/tpl/images/0415/6562/b6d41.png)
So, Cos Ф = ![\dfrac{\textrm 4}{\textrm 5}](/tpl/images/0415/6562/9f520.png)
Now , Since
Cos ( - Ф ) = Cos Ф
So, Cos ( - Ф ) = Cos Ф = ![\dfrac{\textrm 4}{\textrm 5}](/tpl/images/0415/6562/9f520.png)
Hence The value of Cos (-Ф)
. Answer