θ = sin = ·
cos = ·
tan =
csc = · sec = · cot =
Quadrant: | Reference angle:
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Amplitude A:
Phase φ:
Midline D:
Function:
Speed:
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Function:
🎯 Inverse Trig Practice
Type the angle in degrees. (arcsin & arctan answers are in −90…90, arccos in 0…180.)
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🧩 Identity Quiz
What completes the identity?
= ???
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📖 Reference Sheet
Pythagorean: sin²θ + cos²θ = 1 · 1 + tan²θ = sec²θ · 1 + cot²θ = csc²θ Reciprocal: csc θ = 1/sin θ · sec θ = 1/cos θ · cot θ = cos θ/sin θ Quotient: tan θ = sin θ / cos θ Double angle: sin 2θ = 2 sin θ cos θ · cos 2θ = cos²θ − sin²θ Sum: sin(a±b) = sin a cos b ± cos a sin b Sum: cos(a±b) = cos a cos b ∓ sin a sin b Even/Odd: sin(−θ) = −sin θ · cos(−θ) = cos θ · tan(−θ) = −tan θ
Angle θ:
Hypotenuse:
Side a:
Side b:
Angle C: °
Step-by-step solution
📖 The Laws
Law of Sines: a/sin A = b/sin B = c/sin C
Law of Cosines: c² = a² + b² − 2ab·cos C
Use the Law of Cosines when you know two sides and the included angle (SAS),
or all three sides. Otherwise the Law of Sines usually applies.