Question

If the terminal ray of β lies in the fourth quadrant and sin (β) = -√3/3 determine cos(β) in simplest form.

Answer 1

Answer:

cos(β)  = √6/3

Step-by-step explanation:

Given  β lies in the fourth quadrant and sin (β) = -√3/3

we know that the trigonometry formula

sin²(β)+cos²(β) = 1

cos²(β) = 1- sin²(β)

cos²(β) = 1- ( -√3/3)²

           = $1-\frac{3}{9} } } =\frac{6}{9}$

cos(β) =  √6/9 = √6/3

we Know that β lies in the fourth quadrant  so cos(β) is Positive

cos(β)  = √6/3