Trigonometric Functions Calculator
Enter any angle in degrees or radians to get sin, cos, tan, csc, sec, and cot with the working shown.
📐 What is the Trigonometric Functions Calculator?
The trigonometric functions calculator evaluates all six trig functions of an angle in a single step: sine, cosine, tangent, cosecant, secant, and cotangent. You type an angle, choose degrees or radians, and the tool returns every value at once, along with the working that shows how each one is derived. Where a function has no value, such as the tangent of 90 degrees, it clearly reports "undefined" instead of a misleading number.
Students use it to check homework, verify unit-circle values, and see how the reciprocal functions relate to the primary ones. Physics and engineering users reach for it when resolving forces into components, working with waves and oscillations, or converting between degree and radian measure. It is also handy for anyone who needs a quick, exact-looking value without hunting through a scientific calculator's function keys or a printed trig table.
A common source of confusion is the relationship between the three primary functions and their reciprocals. Cosecant is one divided by sine, secant is one divided by cosine, and cotangent is one divided by tangent, which is the same as cosine divided by sine. Because each reciprocal blows up wherever its base function reaches zero, csc and cot are undefined at 0 and 180 degrees, while tan and sec are undefined at 90 and 270 degrees. Recognising this pattern makes the results far easier to interpret.
This tool is useful because it removes the busywork and the sign-and-quadrant slips that come with evaluating trig functions by hand. It accepts any real angle, positive, negative, or larger than a full turn, applies the correct periodic behaviour, and presents six consistent results you can trust and share.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Angle of 30 degrees
Example 2 - Angle of 90 degrees (undefined tan)
Example 3 - Angle of 1 radian
❓ Frequently Asked Questions
🔗 Related Calculators
What are the six trigonometric functions?
They are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Sin, cos, and tan are the primary ratios; csc, sec, and cot are their reciprocals: csc = 1/sin, sec = 1/cos, and cot = 1/tan = cos/sin. This calculator returns all six for any angle.
How do you find sin, cos, and tan of an angle?
On the unit circle, cosine is the x-coordinate and sine is the y-coordinate of the point at angle θ, and tangent is sin θ divided by cos θ. For 30 degrees, sin = 0.5, cos = 0.866025, and tan = 0.577350. Enter the angle and unit, and the calculator computes each value instantly.
Why is tan 90 degrees undefined?
Because tan θ = sin θ / cos θ, and cos 90° = 0. Dividing by zero is undefined, so tangent has a vertical asymptote at 90 and 270 degrees. Secant, which is 1/cos, is undefined at the same angles. The calculator shows 'undefined' rather than a number there.
What is the difference between degrees and radians?
Both measure angles. A full circle is 360 degrees or 2π radians, so 180 degrees equals π radians (about 3.14159). Radians are standard in calculus and physics because they simplify formulas. Use the unit selector to enter either; the calculator displays the angle in both.
What are csc, sec, and cot?
They are the reciprocal trig functions. Cosecant csc θ = 1/sin θ, secant sec θ = 1/cos θ, and cotangent cot θ = 1/tan θ = cos θ/sin θ. They appear often in calculus and physics. Each is undefined wherever its base function equals zero, which the calculator flags automatically.
How do I convert degrees to radians?
Multiply the degree value by π and divide by 180. So 30 degrees = 30 × π / 180 = π/6 ≈ 0.5236 radians, and 90 degrees = π/2 ≈ 1.5708 radians. To go the other way, multiply radians by 180 and divide by π. The calculator shows both forms in its working.
What is the range of sine and cosine?
Both sin θ and cos θ always lie between -1 and 1, inclusive, for any real angle. Tangent and cotangent range over all real numbers, while secant and cosecant have values of 1 or greater in magnitude (they are never between -1 and 1). This is why a sine value above 1 always signals an input error.
Can I use this calculator for angles greater than 360 degrees or negative angles?
Yes. The trig functions are periodic, so the calculator accepts any real angle, positive or negative, and any size. An angle of 405 degrees gives the same values as 45 degrees, and -30 degrees gives the same magnitudes as 30 degrees with signs set by the quadrant.