Trigonometric Identities Calculator
Find trigonometric values from one known value sin²α + cos²α = 1
Choose the known value, enter a number (0.6, 3/5, -sqrt(3)/2…) and the interval containing α. The tool applies the basic identities, explains why the (+) or (−) sign is chosen, and can also compute sin 2α, cos 2α, tan 2α.
The calculator above starts from one known value (sin, cos, tan, or cot) and the quadrant, then uses the fundamental identities to find the other values.
Formulas used
sin²α + cos²α = 1
1 + tan²α = 1/cos²α, tan α · cot α = 1
sin 2α = 2 sin α cos α
- The quadrant decides the sign of the square root.
Worked example
Given sin α = 3/5 with α in quadrant II:
cos α = −4/5, tan α = −3/4, cot α = −4/3
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Enter the known value and choose the quadrant of the angle.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.