Question

The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1

Given sin 0 = 2/5, find cos 0.

cos 0 = ?/?

Answer 1

`\cos \theta =(√(21))/(5)`

Explanation:

Given:

• 
  `\sin \theta=(2)/(5)`

• 
  `(\sin x)^2+(\cos x)^2=1`

Substitute the given value of sin θ into the given identity and solve for cos θ:

`\begin{aligned}(\sin x)^2+(\cos x)^2 & =1\\\implies (\sin \theta)^2+(\cos \theta)^2 & =1\\\left((2)/(5)\right)^2+(\cos \theta)^2 & =1\\\left((2^2)/(5^2)\right)+(\cos \theta)^2 & =1\\(4)/(25)+(\cos \theta)^2 & =1\\(\cos \theta)^2 & =1-(4)/(25)\\(\cos \theta)^2 & =(21)/(25)\\\cos \theta & =\sqrt{(21)/(25)}\\\cos \theta & =(√(21))/(√(25))\\\cos \theta & =(√(21))/(5)\end{aligned}`