Enter angle in degrees or radians:
Calculate sin(12)
sin is found using Opposite/Hypotenuse
Determine quadrant:
Since 0 ≤ 12 ≤ 90 degrees
it is in Quadrant I
sin, cos and tan are positive.
Determine angle type:
12 < 90°, so it is acute
sin(12) = 0.20791169058367
Write sin(12) in terms of cos
Since 12° is less than 90...
We can express this as a cofunction
sin(θ) = cos(90 - θ)
sin(12) = cos(90 - 12)
sin(12) = cos(78)
Excel or Google Sheets formula:
Excel or Google Sheets formula:=SIN(RADIANS(12))Special Angle Values
| θ° | θrad | sin(θ) | cos(θ) | tan(θ) | csc(θ) | sec(θ) | cot(θ) |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | 2 | 2√3/3 | √3 |
| 45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2√3/3 | 2 | √3/3 |
| 90° | π/2 | 1 | 0 | N/A | 1 | 0 | N/A |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 | 2√3/3 | -2 | -√3/3 |
| 135° | 3π/4 | √2/2 | -√2/2 | -1 | √2 | -√2 | -1 |
| 150° | 5π/6 | 1/2 | -√3/2 | -√3/3 | 2 | -2√3/3 | -√3 |
| 180° | π | 0 | -1 | 0 | 0 | -1 | N/A |
| 210° | 7π/6 | -1/2 | -√3/2 | √3/3 | -2 | -2√3/3 | √3 |
| 225° | 5π/4 | -√2/2 | -√2/2 | 1 | -√2 | -√2 | 1 |
| 240° | 4π/3 | -√3/2 | -1/2 | √3 | -2√3/3 | -2 | √3/3 |
| 270° | 3π/2 | -1 | 0 | N/A | -1 | 0 | N/A |
| 300° | 5π/3 | -√3/2 | 1/2 | -√3 | -2√3/3 | 2 | -√3/3 |
| 315° | 7π/4 | -√2/2 | √2/2 | -1 | -√2 | √2 | -1 |
| 330° | 11π/6 | -1/2 | √3/2 | -√3/3 | -2 | 2√3/3 | -√3 |
Show Unit Circle
Final Answer
sin(12) = 0.20791169058367
Test Your Knowledge?
- Angles less than 90° are called _____?
- Angles greater than 90° are called ______?
- In what Quadrant are sin and cos positive?
- In what Quadrant are sin and cos negative?
How does the Trig Measurement Calculator work?
Free Trig Measurement Calculator - Given an angle θ, this calculates the following measurements:
Sin(θ) = Sine
Cos(θ) = Cosine
Tan(θ) = Tangent
Csc(θ) = Cosecant
Sec(θ) = Secant
Cot(θ) = Cotangent
Arcsin(x) = θ = Arcsine
Arccos(x) = θ = Arccosine
Arctan(x) =θ = Arctangent
Also converts between Degrees and Radians and Gradians
Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle
This calculator has 1 input.
Sin(θ) = Sine
Cos(θ) = Cosine
Tan(θ) = Tangent
Csc(θ) = Cosecant
Sec(θ) = Secant
Cot(θ) = Cotangent
Arcsin(x) = θ = Arcsine
Arccos(x) = θ = Arccosine
Arctan(x) =θ = Arctangent
Also converts between Degrees and Radians and Gradians
Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle
This calculator has 1 input.
What 8 formulas are used for the Trig Measurement Calculator?
sin(θ) = Opposite/Hypotenuse
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Coterminal Angles are found by θ ± 360°
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Coterminal Angles are found by θ ± 360°
What 11 concepts are covered in the Trig Measurement Calculator?
- angle
- the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
- cosecant
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)
- cosine
- cos(θ) is the ratio of the opposite side to the hypotenuse.
- cotangent
- The length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)
- coterminal angles
- the angles that have the same initial side and share the terminal sides
- gradian
- defined as one hundredth of the right angle. This is equal to π/200 or 9/10°
- radian
- a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 180°/π ~ 57.3 degrees.
- secant
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- tangent
- the straight line that just touches the curve at that point
- trig measurement
