Question

Sin θ = ____ csc θ = ____ cos θ = ____ sec θ = ____ tan θ = ____ cot θ = ____ Equation of the Circle: _ the unit circle (r = 1), find the value of the six trig ratios:

Answer 1

a. Sin θ = y/r

b. csc θ = r/y

c. cos θ = x/r

d. sec θ = r/x

e. tan θ = y/x

f. cot θ = x/y

g. x² + y² = 1

Explanation:

Where (x, y) are the x and y coordinates of the position with radius r and angle θ measured from the positive x axis. y is the opposite side to the angle θ and x is the adjacent side to the angle θ and r is the hypotenuse side of the right-angled triangle formed by x, y and r. Also, x² + y² = r²

a. Sin θ = opposite/hypotenuse = y/r

b. csc θ = hyotenuse/opposite = 1/Sin θ = r/y

c. cos θ = adjacent/hypotenuse = x/r

d. sec θ = hypotenuse/adjacent = 1/cos θ = r/x

e. tan θ = opposite/adjacent = y/x

f. cot θ = adjacent/opposite = 1/tan θ = x/y

g. Equation of the Circle: _ the unit circle (r = 1),

Since x² + y² = r² ,for a unit circle, r = 1. So,

x² + y² = 1²

x² + y² = 1