Let sinx=2/3, how do you show that f(2x)=-(4sqrt5)/9? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer salamat Mar 14, 2017 see explanation below Explanation: sin x = 2/3, therefore by using Pythagoras theorem, cos x = sqrt 5/3 if f(x) = sin x, then f(2 x) = sin 2 x sin 2 x = 2 sin x cos x sin 2 x = 2 * 2/3 *sqrt 5/3 therefore, f (2 x) =sin 2 x = (4 sqrt 5)/9 Answer link Related questions What does it mean to find the sign of a trigonometric function and how do you find it? What are the reciprocal identities of trigonometric functions? What are the quotient identities for a trigonometric functions? What are the cofunction identities and reflection properties for trigonometric functions? What is the pythagorean identity? If sec theta = 4, how do you use the reciprocal identity to find cos theta? How do you find the domain and range of sine, cosine, and tangent? What quadrant does cot 325^@ lie in and what is the sign? How do you use use quotient identities to explain why the tangent and cotangent function have... How do you show that 1+tan^2 theta = sec ^2 theta? See all questions in Relating Trigonometric Functions Impact of this question 3536 views around the world You can reuse this answer Creative Commons License