त्रिकोणमिति कैलकुलेटर

Asteet vai radiaanit?

Trigonometric functions can be calculated in either degrees or radians, and the wrong unit is the most common source of error. A full circle is 360°, i.e. 2π radians, so for example 180° corresponds to π radians. Select the correct unit at the top before calculating — the calculator always gives the result in the selected unit.

कैलकुलेटर कैसे उपयोग करें

1. Choose the angle unit. Degrees° or radians from the buttons.
2. Choose the function. sin, cos, tan or an inverse function arcsin/arccos/arctan.
3. Enter the angle or value. You can also tap a ready-made angle from 30° to 180°.
4. Calculate. The result appears immediately. With inverse functions the input is a ratio −1…1 (arcsin, arccos).

What is trigonometry needed for?

Trigonometry describes the relationships between angles and sides and is central to physics, engineering, construction and navigation. Angles are used to calculate heights, distances and the components of forces. In upper secondary mathematics, sine, cosine and tangent and their inverse functions are constantly in use, for example in solving triangles and modelling periodic phenomena.

Example: a side of a right triangle

In a right triangle, the acute angle is 35° and the hypotenuse is 10. How long is the side opposite the angle? We use sine, because sine = opposite side / hypotenuse. So the opposite side = 10 · sin(35°) = 10 · 0.5736 ≈ 5.74. The adjacent side would come from cosine: 10 · cos(35°) ≈ 8.19. Thus trigonometric functions connect angles and sides, and the calculator gives the values immediately in the selected angle unit.

Yksikköympyrä ja etumerkit

In the unit circle, an angle corresponds to a point whose x-coordinate is the cosine and y-coordinate the sine. In the first quadrant (0–90°) both sine and cosine are positive. In the second quadrant (90–180°) sine stays positive but cosine becomes negative. This explains why, for example, cos(120°) is negative. The tangent is the quotient of sine and cosine, so it is undefined whenever cosine is zero, as at 90° and 270°.

Why is the radian a natural unit?

The degree is a human-agreed unit: the full circle was divided into 360 parts already in ancient Babylon. The radian, on the other hand, is based on the circle's own geometry. One radian is the angle whose arc is as long as the circle's radius, and the whole circumference is 2π radii — that is why a full turn is 2π radians. This makes the radian a "natural" unit for many formulas.

In higher mathematics and physics, radians are the default unit because they simplify formulas: for example, the derivative and series expansions take a clean form only with radians. Everyday angles and triangle problems, on the other hand, are often expressed in degrees. This calculator lets you choose, so you can use the unit that suits the task, and the conversion via π/180 is always at hand.

Good to know about trigonometry

• The values of sine and cosine are always between −1 and 1; the tangent can take any value.
• The basic identity sin²x + cos²x = 1 holds for all angles and is a useful check.
• The functions are periodic: sine and cosine repeat every 360° (2π).
• For inverse functions the input is a ratio, not an angle — arcsin and arccos require a value between −1 and 1.

संक्षेप में

The trigonometry calculator gives sine, cosine and tangent and the inverse functions in degrees or radians. Choose the angle unit, enter the angle or ratio and read the result immediately. Remember that the wrong angle unit is the most common source of error — the calculator shows the selected mode clearly and always computes the result accordingly.

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