Question

Let sin(−θ)=−3/5 and tanθ>0. What is the value of cos(−θ)?

Answer 1

Answer:

The value of  Cos (-Ф) $\dfrac{\textrm 4}{\textrm 5}$ .

Step-by-step explanation:

Given Trigonometric function as :

sin( - Ф ) = $\frac{- 3}{5}$

- sin Ф = $\frac{- 3}{5}$

So, sin Ф = $\frac{ 3}{5}$

Now, as sin Ф = $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$

So ,  $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$ =  $\frac{ 3}{5}$

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 = $\sqrt{16}$

I.e Base = 4

Now, Cos Ф =  $\dfrac{\textrm base}{\textrm hypotenuse}$

So, Cos Ф =  $\dfrac{\textrm 4}{\textrm 5}$

Now , Since

Cos ( - Ф ) = Cos Ф

So,  Cos ( - Ф ) = Cos Ф =  $\dfrac{\textrm 4}{\textrm 5}$

Hence The value of  Cos (-Ф) $\dfrac{\textrm 4}{\textrm 5}$ . Answer