Pythagorist
Trigonometry

Sin Cos Tan Calculator

Calculate the sine, cosine, and tangent of any angle instantly. Enter an angle in degrees or radians and see all three trigonometric ratios with full step-by-step working shown.

sin

0.5

cos

0.866025

tan

0.57735

How it works

  1. Convert to radians

    30°×π180=0.523599 rad30° \times \frac{\pi}{180} = 0.523599 \text{ rad}

    30° = 0.523599 radians.

  2. Calculate sin

    sin⁡(30°)=0.5\sin(30°) = 0.5

    sin(30°) = 0.5.

    Result:0.5

  3. Calculate cos

    cos⁡(30°)=0.866025\cos(30°) = 0.866025

    cos(30°) = 0.866025.

    Result:0.866025

  4. Calculate tan

    tan⁡(30°)=0.57735\tan(30°) = 0.57735

    tan(30°) = 0.57735.

    Result:0.57735

Sin, Cos, Tan Definitions

sin⁡θ=oppositehypotenuse,cos⁡θ=adjacenthypotenuse,tan⁡θ=oppositeadjacent\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan\theta = \frac{\text{opposite}}{\text{adjacent}}
θθThe angle in degrees or radians
oppositeoppositeThe side opposite to the angle
adjacentadjacentThe side next to the angle (not the hypotenuse)
hypotenusehypotenuseThe longest side, opposite the right angle

Example substitution

sin⁡(30°)=0.5,cos⁡(30°)≈0.866,tan⁡(30°)≈0.577\sin(30°) = 0.5, \quad \cos(30°) \approx 0.866, \quad \tan(30°) \approx 0.577

For 30°: sin = 0.5, cos ≈ 0.866, tan ≈ 0.577.

Worked examples

Find sin, cos, and tan of 45°.

  1. 1
    Convert to radians: 45° × π/180 = 0.7854 rad
  2. 2
    Calculate sin: sin(45°) = 0.707107
  3. 3
    Calculate cos: cos(45°) = 0.707107
  4. 4
    Calculate tan: tan(45°) = 1
Answer: sin = 0.707107, cos = 0.707107, tan = 1

Find sin, cos, and tan of 60°.

  1. 1
    Convert to radians: 60° × π/180 = 1.0472 rad
  2. 2
    Calculate sin: sin(60°) = 0.866025
  3. 3
    Calculate cos: cos(60°) = 0.5
  4. 4
    Calculate tan: tan(60°) = 1.732051
Answer: sin = 0.866025, cos = 0.5, tan = 1.732051

Find sin, cos, and tan of 90°.

  1. 1
    Convert to radians: 90° × π/180 = 1.5708 rad
  2. 2
    Calculate sin: sin(90°) = 1
  3. 3
    Calculate cos: cos(90°) = 0
  4. 4
    Calculate tan: tan(90°) = undefined (division by zero)
Answer: sin = 1, cos = 0, tan = undefined

Frequently asked questions

What is SOHCAHTOA?+

A mnemonic for trigonometric ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

What is sin 30°?+

sin 30° = 0.5 (exact value: 1/2).

What is cos 45°?+

cos 45° = √2/2 ≈ 0.7071.

How do you find an angle using trigonometry?+

Use the inverse function. If sin(θ) = 0.5, then θ = sin⁻¹(0.5) = 30°.

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