Question

If 0°<0<90° and sin0=12/13, find cos0 using trigonometric identities.

• 12/5
• 5/12
• 12/13
• 5/13

Answer 1

here's the solution,

we know :

`\sin( \theta) = (perpendicular)/(hypotenuse)`

So,

`(p)/(h) = (12)/(13)`

so.. let the perpendicular be 12x and hypotenuse be 13x

now,

by applying pythagoras theorem,

• 
  `b {}^(2) = h {}^(2) - p {}^(2)`

where,

• b = base
• h = hypotenuse
• p = perpendicular

So,

• 
  `b {}^(2) = ({13x})^(2) - ({12x})^(2)`
• 
  `b {}^(2) = 169x {}^(2) - 144x {}^(2)`
• 
  `{b}^(2) = 25x {}^(2)`
• 
  `b = 5x`

so,

• 
  `\cos( \theta) = (b)/(h)`

• 
  `\cos( \theta) = (5x)/(13x)`

• 
  `\cos( \theta) = (5)/(13)`

hope it helps !!