Find sin β if cos β =12/13

Question

I have forgotten hot to solve for problems like this,

Answer 1

Use the trigonometric identity

 

sin²β + cos²β = 1

 

sinβ = √(1 - cos²β) = √[1 - (12/13)²] = √(25/169) = ±5/13

 

There is not sufficient information given to decide whether β is in quadrant I or IV, since cosβ is positive in both quadrants.

Answer 2

Sin = ?? sin = Perp. ÷ hyp.
cos = Base ÷ hypotinous
Base =12 , hyp = 13
pathogras theoram
square of hyp - square of base = square of Perp.

Perp. = 5

 

so

sin = 5/13 

or you can write in thus way

sin  = 5 ÷ 13

Answer 3

Use the Pythagorean Identity  sin²x + cos²x = 1.

 

The answer will be 5/13...based on the Reference Triangle's 5,12,13 side lengths.  (This is based on first quadrant only)