Solve the Problem $\sin \theta$ , Given That $\cos 2 \theta = \frac { 1 } { 4 }$

question 2

Multiple Choice

Solve the problem.
-Find $\sin \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$ .

• A) \(\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }\)
• B) \(\frac { \sqrt { 10 - 2 \sqrt { 6 } } } { 4 }\)
• C) \(\frac { \sqrt { 6 } } { 4 }\)
• D) \(\frac { \sqrt { 10 } } { 4 }\)

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Definitions:

Posterior Leg Muscles

Muscles located at the back of the leg that are primarily involved in movement and stabilization of the ankle, foot, and toes.

Extensor Digitorum Longus

The extensor digitorum longus is a muscle in the lower leg that helps to extend the toes and the foot.

Range Of Motion

The full movement potential of a joint, usually its range of flexion and extension; important in assessing flexibility and mobility.

Lower Limb

The part of the body extending from the hip to the toes, including the thigh, leg, and foot.