Online trig identities calculator: given sin x, find cos x via the Pythagorean identity and tan x via the ratio identity; the foundation of trigonometric manipulation.
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sin²x+cos²x=1, tan x=sin x/cos x
Quadrant I, cos positive; |sin|≤1
📖 Tutorial | Identities
1. Definition
For the same angle x: the Pythagorean identity sin²x+cos²x=1 and the ratio identity tan x=sin x/cos x, derived from the unit circle, hold for every angle.
2. Formula & Notation
sin x
Sine
cos x
Cosine
tan x
Tangent
3. Properties & Laws
sin²x+cos²x=1;
tan x=sin x/cos x (cos x≠0);
Reciprocals: csc=1/sin, sec=1/cos, cot=1/tan;
1+tan²x=sec²x.
4. Steps
Enter sin x (Quadrant I, cos positive);
Click "Calculate" for cos, tan;
Or click "Load Example".
5. Worked Examples
Example: sin x=0.6 gives cos x=√0.64=0.8 and tan x=0.75.
6. Common Pitfalls
The sign of cos depends on the quadrant; tan is undefined when cos=0; sin²x means (sin x)².