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Sin 45 Degrees

sin(45°) = 0.70710678, exactly √2/2.

Answer

sin(45°) = 0.70710678, exactly √2/2. The angle 45° equals π/4 radians (45 × π/180).

Exact form: √2/2. Decimal: 0.70710678 (rounded to 8 places).

Where 45° sits on the unit circle

45° lies quadrant I. Remember that sine is positive in quadrants I and II, and negative in the others, which decides the sign of the answer.

How to calculate sin 45° on a scientific calculator

  1. Set the calculator to DEG (degrees) mode.
  2. Press sin.
  3. Type 45.
  4. Press = to get 0.70710678.

If you get a different number, the calculator is probably in RAD mode. In radians you would enter π/4 instead of 45.

Quick results

sin 45°= 0.70710678
cos 45°= 0.70710678
tan 45°= 1

Sin of common angles

AngleRadiansSin
0°00
30°π/60.5
45°π/40.707107
60°π/30.866025
90°π/21
120°2π/30.866025
135°3π/40.707107
150°5π/60.5
180°π0
270°3π/2-1
360°2π0

Frequently Asked Questions

What is sin 45 degrees?

sin(45°) = 0.70710678, exactly √2/2.

What is sin 45° in radians?

45° = π/4 radians, so sin(45°) = sin(π/4) = 0.70710678.

Why does my calculator show a different answer for sin 45?

It is most likely set to radians. Switch to degree (DEG) mode before entering the angle.

Is sin 45° positive or negative?

Positive.

Is there an online scientific calculator I can use for this?

Yes. Use the calculator on this page, or open the full free Scientific Calculator with memory, history and keyboard support.

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