Question

Find sin θ if cos θ = 4/7 and θ in quadrant IV.

Answer 1

Answer:

sinΘ = - $\frac{\sqrt{33} }{7}$

Step-by-step explanation:

Using the trigonometric identity

sin²Θ + cos²Θ = 1, thus

sinΘ = ± $\sqrt{1-cos^20}$

Since Θ is in the fourth quadrant then sinΘ < 0

Given

cosΘ = $\frac{4}{7}$ , then

sinΘ = - $\sqrt{1-(\frac{4}{7})^2 }$ = - $\sqrt{1-\frac{16}{49} }$ = - $\sqrt{\frac{33}{49} }$ = - $\frac{\sqrt{33} }{7}$