θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
-$$\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$$
A) $\frac { 1 } { 3 }$
B) $2 \sqrt { 2 }$
C) 3
D) $\frac { 3 \sqrt { 2 } } { 4 }$ Use an identity to find the value of the expression. Do not use a calculator.

Question

Quizplus · Accepted Answer

Given $\sin \theta = \frac{2\sqrt{2}}{3}$, we can find $\cos \theta$ using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$. Solving for $\cos \theta$, we get $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - \left(\frac{2\sqrt{2}}{3}\right)^2} = \sqrt{1 - \frac{8}{9}} = \sqrt{\frac{1}{9}} = \frac{1}{3}$.

θ Is an Acute Angle and Sin θ and Cos sin⁡θ=223\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }sinθ=322​​

θ Is an Acute Angle and Sin θ and Cos $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$