# What is the difference between Sines and cosines?

What is the difference between Sines and cosines? Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What are the 3 laws of cosine? a2 = b2 + c2 – 2bc cos A and b2 = a2 + c2 – 2ac cos B. Since the three verions differ only in the labelling of the triangle, it is enough to verify one just one of them. We’ll consider the version stated first.

Is SAS law of sines or Law of Cosines? “SAS” is when we know two sides and the angle between them. use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

How do you do law of sines?

## What is the difference between Sines and cosines? – Additional Questions

### What is the formula sin?

What Is the Sin Formula? The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse. sin(θ + 2nπ) = sin θ for every θ

### How do you know when to use the law of sines?

The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

### Does law of sines work for all triangles?

Sine Rule. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. You will only ever need two parts of the Sine Rule formula, not all three. You will need to know at least one pair of a side with its opposite angle to use the Sine Rule.

### What is cosine law used for?

The cosine law is used to determine the third side of a triangle when we know the lengths of the other two sides and the angle between them.

### When should you use law of cosines?

Use the law of cosines when you are given SAS, or SSS, quantities. For example: If you were given the lengths of sides b and c, and the measure of angle A, this would be SAS. SSS is when we know the lengths of the three sides a, b, and c.

### Which cases can use Law of Cosines?

1 Answer. The Law of Cosine can only be used if two sides and their enclosed angle are known. In all other cases the Law of Sines has to be used.

### Which case Cannot be solved using laws of Sines?

If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we cannot use the Law of Sines because we cannot set up any proportions where enough information is known.

### How do you know if a triangle is cos?

In any right angled triangle, for any angle:
1. The sine of the angle = the length of the opposite side. the length of the hypotenuse.
2. The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
3. The tangent of the angle = the length of the opposite side. the length of the adjacent side.

### Why is sine called sine?

In trigonometry, the name “sine” comes through Latin from a Sanskrit word meaning “chord”. In the picture of a unit circle below, AB has length sinθ and this is half a chord of the circle. The co-functions are functions of complementary angles: cosθ = sin(π/2 − θ), cotθ = tan(π/2 − θ), and cscθ = sec(π/2 − θ).