Trigonometric identities: Pythagorean and quotient
Use the Pythagorean identity or the quotient identity to find a missing trig ratio for an acute angle. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Angle theta is acute, and sin(theta) = 3/5. Use the Pythagorean identity to find cos(theta).
Answer: 4/5
See one solved, step by step
Angle theta is acute, and sin(theta) = 20/29. Use the Pythagorean identity to find cos(theta).
📘 Worked solution
1sin2(theta) + cos2(theta) = 1This is the Pythagorean identity — true for every angle theta.
2(2029)2 + cos2(theta) = 1Substitute the given value of sin(theta).
3cos2(theta) = 1 - 400841 = 441841Isolate cos^2(theta): 29^2 - 20^2 = 441 = 441.
4cos(theta) = √(441841) = 2129theta is acute, so cos(theta) is positive — take the positive square root.
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