Why is cos(4pi/3) = - cos(pi/3)? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Shwetank Mauria May 2, 2016 Please see below. Explanation: #cos(4pi/3)=cos(pi+pi/3)# Now using #cos(A+B)=cosAcosB-sinAsinB#, the above is equal to #cospicos(pi/3)-sinpisin(pi/3)# = #(-1)xxcos(pi/3)-0xxsin(pi/3)# = #-cos(pi/3)# 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 3006 views around the world You can reuse this answer Creative Commons License