Trigonometric Functions Calculator (Degrees)

Enter Calculation

Function sin θ cos θ tan θ sin, cos, tan csc θ sec θ cot θ csc, sec, cot All six

Angle θ (degrees) Enter 5.25 for 5.25 degrees; enter 5'12'6 for 5 degrees 12 minutes 6 seconds.

Digits 6 10 14 18 22 26 30 34 38 42 46 50

Formula

Show calculation steps (1)

1. Reciprocal functions

   

   Cosecant, secant and cotangent are reciprocals of sine, cosine and tangent.

Results

Angle θ

5.201667°

decimal degrees

Function	Value
sin θ	0.09066154926231
cos θ	0.99588176179974
tan θ	0.09103645908573
csc θ	11.03003432146026
sec θ	1.00413526821981
cot θ	10.98461001276747

What it is

This trigonometric functions calculator computes all six trig ratios — sine, cosine, tangent, cosecant, secant, and cotangent — for an angle entered in DEGREES. The angle may be a plain decimal value (5.25) or in degrees-minutes-seconds (DMS) notation (5'12'6). It is a pure-math tool that applies identically everywhere.

On the unit circle, the angle theta gives a point whose coordinates are (cos theta, sin theta).

How to use it

Enter your angle in the Angle field. For a decimal angle type the number directly, e.g. 45 or 5.25. For DMS, separate degrees, arc-minutes and arc-seconds with apostrophes: 5'12'6 means 5 degrees, 12 minutes, 6 seconds. Choose how many display digits you want, then read off the six ratios. Undefined values (such as tan 90 degrees) are shown as "undefined".

The formula explained

The angle in degrees is first converted to decimal degrees (degrees + minutes/60 + seconds/3600) and then to radians using \(\theta_{rad}=\theta_{deg}\cdot\frac{\pi}{180}\). From sin and cos the rest follow:

$$\sin\theta=\sin\!\left(\theta\cdot\frac{\pi}{180}\right),\quad \cos\theta=\cos\!\left(\theta\cdot\frac{\pi}{180}\right),\quad \tan\theta=\frac{\sin\theta}{\cos\theta}$$

The reciprocal ratios are

$$\csc\theta=\frac{1}{\sin\theta},\ \sec\theta=\frac{1}{\cos\theta},\ \cot\theta=\frac{\cos\theta}{\sin\theta}$$

Reciprocal functions are undefined where their denominator is zero, so tan and sec are undefined at 90 and 270 degrees, while csc and cot are undefined at 0 and 180 degrees.

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In a right triangle, the six trig functions are ratios of the opposite, adjacent and hypotenuse sides.

Worked example

For 5'12'6 the decimal angle is

$$5 + \frac{12}{60} + \frac{6}{3600} = 5.2016666667 \text{ degrees}$$

In radians that is \(0.0907866\). Then \(\sin = 0.090661937\), \(\cos = 0.995882104\) and \(\tan = 0.091036699\).

FAQ

Is the angle in degrees or radians? Degrees. The tool converts to radians internally before computing.

Why does tan 90 show undefined? Because cos 90 degrees is zero, and tangent equals sine divided by cosine, so it is mathematically undefined.

Can I enter negative or very large angles? Yes. Trig functions are periodic, so any real angle works; a leading minus sign applies to the whole DMS magnitude.