Complementary angles
- Input
- sen 30° e cos 60°
- Expected output
- ambos 0,5
30° and 60° add up to 90°: sin(30°)=cos(60°) whenever the two angles are complementary, a symmetry, not a coincidence.
Carregando ferramenta… / Loading tool…
sine cosine and tangent
Sine, cosine and tangent of an angle come from the point (cos θ, sin θ) on the unit circle, and three angles have exact values worth memorizing: 30°, 45° and 60°. But the same number, like 30, produces completely different results depending on whether the unit is degrees or radians, a detail that wrecks the calculation if it goes unnoticed.
30° and 60° add up to 90°: sin(30°)=cos(60°) whenever the two angles are complementary, a symmetry, not a coincidence.
30 radians is almost 4.77 full turns, landing in the fourth quadrant (≈278.87°); the wrong unit even flips the sign of the result.
Dividing sin by cos=0 has no real result; at 270° the same undefined case repeats, whenever the point falls on the circle's vertical axis.
It's the circle of radius 1 centered at the origin. For an angle measured from the x-axis, the point on the circle has coordinates (cos θ, sin θ), giving the trig functions a geometric meaning.
It is the mnemonic for the three ratios in a right triangle: Sine = Opposite÷Hypotenuse, Cosine = Adjacent÷Hypotenuse, Tangent = Opposite÷Adjacent. It only works for angles between 0° and 90°; outside that range, the unit-circle definition, (cos θ, sin θ), still holds even when there is no right triangle left to draw.
Because tangent is sin÷cos, and cos 90° = 0: dividing by zero has no real result, so the tool returns null instead of a number at that angle and at any other where cos is zero, like 270°.
Yes, and the difference can be drastic: 30° is an acute angle with sin 0.5, but 30 radians correspond to almost 4.77 full turns, landing at ≈278.87° in the fourth quadrant, with sin ≈ −0.988. Always check which unit the calculator's toggle is set to before reading the result.
Calculations run in your browser. No data is sent to a server.