त्रिकोणमिती कॅल्क्युलेटर: sin, cos, tan आणि व्यस्त फलने

अंश, रेडियन किंवा ग्रेडियनमध्ये sin, cos, tan, sec, csc व cot काढा. 15° च्या पटींना अचूक मूल्ये आणि व्यस्त फलनांची सर्व उत्तरे पाहा.

अद्यतनित २८ सप्टेंबर, २०२६तपासलेली उदाहरणे: १३

निकाल

कमाल दशांश स्थाने: १०; जवळचे मूल्य; समान अंतरावर शून्यापासून दूर

अचूक मूल्य: 1/2
cos: 0.8660254038
tan: 0.5773502692
sec: 1.1547005384
csc: 2
cot: 1.7320508076
Angle in radians: 0.5235987756rad
Reference angle: 30°
Position: Quadrant I

sin 30° = 0.5 (exactly 1/2). The angle sits in Quadrant I, where the point on the unit circle is (0.866, 0.5).

Unit circle

All six functions at 30° ओळी: ६

Function	मूल्य	अचूक
sin	0.5	1/2
cos	0.866	√3/2
tan	0.5774	√3/3
sec	1.1547	2√3/3
csc	2	2
cot	1.7321	√3

गणना कशी केली जाते S

कोन
$30^\circ$
Position on the unit circle
Quadrant I; reference angle 30°.
Sine and cosine
$\sin\theta = 0.5,\qquad \cos\theta = 0.8660254038$
sin from sine and cosine
$\sin\theta = 0.5$
Exact: sin 30° = 1/2.

त्रिकोणमिती कॅल्क्युलेटर: sin, cos, tan आणि व्यस्त फलने बद्दल

Enter an angle in degrees, radians or gradians to get all six trigonometric functions. Sine and cosine are the coordinates of the matching point on the unit circle; the rest follow as tan = sin/cos, sec = 1/cos, csc = 1/sin and cot = cos/sin. At multiples of 15° the exact surd form is shown as well, such as sin 60° = √3/2. The inverse mode turns a value back into an angle and lists every angle that shares it.

The default, sin 30°, is exactly 1/2, and the drawing puts the point at (0.866, 0.5). The same functions convert between angles and slopes: a roof pitched at 37° rises tan 37° = 0.7536 m per metre of run.

Principal values follow the NIST Digital Library of Mathematical Functions: arcsin and arctan return −90° to 90°, arccos 0° to 180°. arccot uses the continuous range 0° to 180°, which differs from the DLMF definition for negative inputs.

सोडवलेली उदाहरणे

sin 30°

I want: Function of an angle
Function: sin
कोन: 30
Angle unit: अंश

निकाल: 0.5
अचूक मूल्य: 1/2
cos: 0.8660254038

पडताळणीचा स्रोत: Standard special value (A&S Table 4.3); Python 3.8 math: cos(radians(30))

tan 45°

I want: Function of an angle
Function: tan
कोन: 45
Angle unit: अंश

निकाल: 1
अचूक मूल्य: 1
sec: 1.4142135624

पडताळणीचा स्रोत: Standard special value; Python 3.8 math: 1/cos(pi/4)

cos 120° (second quadrant)

I want: Function of an angle
Function: cos
कोन: 120
Angle unit: अंश

निकाल: -0.5
अचूक मूल्य: −1/2
Reference angle: 60 °
Position: Quadrant II

पडताळणीचा स्रोत: cos(180° − 60°) = −cos 60° = −1/2

sin(π/4) in radians

I want: Function of an angle
Function: sin
कोन: pi/4
Angle unit: रेडियन

निकाल: 0.7071067812
अचूक मूल्य: √2/2
Angle in degrees: 45 °

पडताळणीचा स्रोत: Python 3.8 math: sin(pi/4) = √2/2

प्रश्न

How do you convert degrees to radians?

Multiply by π/180: 30° is π/6 ≈ 0.5236 rad, 45° is π/4 ≈ 0.7854 rad and 180° is π rad. To go back, multiply radians by 180/π ≈ 57.2958. Mixing the two is the most common trig mistake: sin 30 with the angle read as radians is −0.988, not 0.5.

What are the exact values of sin, cos and tan at 30°, 45° and 60°?

sin 30° = 1/2, sin 45° = √2/2 ≈ 0.7071 and sin 60° = √3/2 ≈ 0.8660; cosine takes the same values in reverse order, so cos 30° = √3/2 and cos 60° = 1/2. tan 30° = √3/3 ≈ 0.5774, tan 45° = 1 and tan 60° = √3 ≈ 1.7321. All of them come from the 30-60-90 and 45-45-90 triangles.

Why is tan 90° undefined?

Because tan θ = sin θ / cos θ and cos 90° = 0, so the ratio divides by zero. As θ approaches 90° from below, tan θ grows without bound: tan 89° ≈ 57.29 and tan 89.9° ≈ 572.96. The same happens at 270° and every 90° + 180°k. Secant is undefined at those angles too, and cosecant and cotangent wherever sin θ = 0.

Is sin⁻¹ the same as 1/sin?

No. sin⁻¹ x, also written arcsin x, is the inverse function: the angle whose sine is x, so sin⁻¹ 0.5 = 30°. 1/sin x is the reciprocal, called cosecant: csc 30° = 1/0.5 = 2. The clash arises because sin² x means (sin x)², while the −1 exponent on a function name means its inverse; writing arcsin avoids the ambiguity.

Why does arcsin give only one angle?

A function must return a single value, so arcsin is restricted to a principal range of −90° to 90° (DLMF §4.23). Every other angle with the same sine follows from θ and 180° − θ plus whole turns: sin θ = 0.5 for θ = 30° + 360°k or 150° + 360°k, with k any integer. For arccos the range is 0° to 180° and the other family is −θ + 360°k.

“त्रिकोणमिती कॅल्क्युलेटर: sin, cos, tan आणि व्यस्त फलने” किती अचूक आहे?

अचूकता तुमच्या इनपुटवर आणि पद्धतीच्या गृहीतकांवर अवलंबून असते. दशांश गणना 50 सार्थ अंक वापरते, पण अंदाज, संख्यात्मक पद्धती आणि मूळ डेटा कमी अचूक असू शकतात; दाखवलेल्या मूल्यांचे पूर्णांकन केल्याने या मर्यादा दूर होत नाहीत. स्वतंत्र स्रोतांतील सोडवलेल्या उदाहरणांशी पडताळणी: १३. उदाहरणार्थ, “sin 30°” ची पडताळणी Standard special value (A&S Table 4.3); Python 3.8 math: cos(radians(30)) याच्याशी केली आहे.

या पद्धतीचा स्रोत कोणता?

NIST Digital Library of Mathematical Functions §4.14 (definitions) and §4.23 (inverse trigonometric functions, principal values); Abramowitz & Stegun, Handbook of Mathematical Functions, Table 4.3 — special values of the trigonometric functions.

या कॅल्क्युलेटरबद्दल

\sec\theta = \frac{1}{\cos\theta},\quad \csc\theta = \frac{1}{\sin\theta},\quad \cot\theta = \frac{\cos\theta}{\sin\theta},\quad 1^\circ = \frac{\pi}{180}\,\text{rad} = \frac{10}{9}\,\text{grad}

स्रोत

NIST Digital Library of Mathematical Functions §4.14 (definitions) and §4.23 (inverse trigonometric functions, principal values)
Abramowitz & Stegun, Handbook of Mathematical Functions, Table 4.3 — special values of the trigonometric functions

संदर्भांशी पडताळलेले

या कॅल्क्युलेटरमध्ये स्वतंत्र स्रोतांमधील उत्तरांसह १३ सोडवलेली उदाहरणे आहेत. ती चाचणी संचात चालतात आणि तुम्ही ती येथेही चालवू शकता.