If sin theta + cos theta =p, what is sin^2 theta + cos^4theta in terms of p ? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Cesareo R. Feb 22, 2017 1-((p^2-1)/2)^2 Explanation: (sintheta+costheta)^2= 1+2sinthetacostheta = p^2 so sinthetacostheta = (p^2-1)/2 now sin^2theta+cos^4theta=sin^2theta+(1-sin^2theta)cos^2theta=1-sin^2thetacos^2theta and putting all together sin^2theta+cos^4theta = 1-((p^2-1)/2)^2 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 7667 views around the world You can reuse this answer Creative Commons License