We are asked to fill in the blank in the following formula.
sin θ =
To do so, we need to recall the definitions of trigonometric functions of any angle. Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and r=sqrt(x^2+y^2)≠0.
Then, we can find the values of all six trigonometric functions using the following formulas.
Definitions of Trigonometric Functions of Any Angle
sin θ = y/r
cos θ = x/r
tan θ = y/x, x ≠0
cot θ = x/y, y ≠0
sec θ = r/x, x ≠0
csc θ = r/y, y ≠0
Let's take a closer look at the table and find the formula containing the expression sin θ.
Definitions of Trigonometric Functions of Any Angle
sin θ = y/r
cos θ = x/r
tan θ = y/x, x ≠0
cot θ = x/y, y ≠0
sec θ = r/x, x ≠0
csc θ = r/y, y ≠0
According to the table, sin θ = yr. With this in mind, let's fill in the blank.
sin θ = yr
