What is the range of inverse trig functions?

arcsin: [-90°, 90°], arccos: [0°, 180°], arctan: (-90°, 90°). These are the principal value ranges. Note: arcsin(0.5) = 30°, arccos(0.5) = 60°, arctan(1) = 45°.

Trigonometry Calculator – Sin, Cos, Tan with Steps

Q: What are the six trigonometric ratios?

The six trig ratios are: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.

Q: What are the standard trigonometric values?

sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1. cos is sin in reverse order. tan 0°=0, tan 30°=1/√3, tan 45°=1, tan 60°=√3, tan 90°=undefined.

Q: How do you convert degrees to radians?

Radians = Degrees × π / 180. Examples: 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. To convert radians to degrees: Degrees = Radians × 180 / π.

Q: Where does trigonometry appear in competitive exams?

Trigonometry questions in SSC CGL, CHSL, and Railway exams cover: standard values (sin/cos/tan of 0°,30°,45°,60°,90°), identities like sin²θ + cos²θ = 1, height and distance problems, and simplification of trig expressions.

Enter an angle to get all six trigonometric ratios: sin, cos, tan, cosec, sec, cot.

Angle

Unit

Please enter a valid angle.

Enter a value to find arcsin, arccos, or arctan — result in degrees and radians.

Value

Function

For arcsin/arccos value must be between −1 and 1.

Standard trigonometric values for angles 0°, 30°, 45°, 60° and 90°.

Angle	sin	cos	tan	cosec	sec	cot
0°	0	1	0	∞	1	∞
30°	1/2	√3/2	1/√3	2	2/√3	√3
45°	1/√2	1/√2	1	√2	√2	1
60°	√3/2	1/2	√3	2/√3	2	1/√3
90°	1	0	∞	1	∞	0

Memory trick for sin: sin 0°=√0/2, sin 30°=√1/2, sin 45°=√2/2, sin 60°=√3/2, sin 90°=√4/2. Simplify each: 0, 1/2, 1/√2, √3/2, 1.

Key identities: sin²θ + cos²θ = 1 | 1 + tan²θ = sec²θ | 1 + cot²θ = cosec²θ

How to Use

Choose Mode

Use Trig Ratios for all six values of an angle, Inverse Trig to find an angle from a ratio, or Standard Values for the exam-ready table.

Enter Angle or Value

Enter the angle in degrees or radians. For inverse, enter a decimal value (e.g. 0.5 for arcsin).

Get All Six Ratios

See sin, cos, tan, cosec, sec, cot — with quadrant, degree↔radian conversion, and step-by-step notes.

Frequently Asked Questions

What are the six trigonometric ratios?

What are the standard trigonometric values?

sin: 0°=0, 30°=½, 45°=1/√2, 60°=√3/2, 90°=1. cos is the reverse. tan: 0°=0, 30°=1/√3, 45°=1, 60°=√3, 90°=undefined. Memory trick: sin values follow √0/2, √1/2, √2/2, √3/2, √4/2.

How do you convert degrees to radians?

Radians = Degrees × π/180. Key values: 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π. To reverse: Degrees = Radians × 180/π.

What are the three Pythagorean identities?

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = cosec²θ

These are derived from the Pythagorean theorem and are the most frequently used identities in SSC and competitive exam questions.

Where does trigonometry appear in competitive exams?

SSC CGL, CHSL, and Railway exams cover: standard values (0°–90°), Pythagorean identities, complementary angle identities (sin θ = cos(90°−θ)), height & distance problems, and simplification of trig expressions using identities.

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