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. Study the triangle ABC shown below.
How do I know if I need Sin Cos or tan?
If the opposite and hypotenuse are being used, use sine for the calculations
. If the adjacent and hypotenuse are used, use cosine. If the opposite and adjacent are being used, use tangent. You can remember this using the acronym SOH CAH TOA.
Why do we use Cos instead of sin?
In this case, the exercise says it is an angle with the horizontal, so
a cosine will give you the horizontal component (adjacent to the angle)
, while sine will give you the y-component (opposite to the angle).
What is cos sin equal to?
| Sine Function: sin(θ) = Opposite / Hypotenuse | Cosine Function: cos(θ) = Adjacent / Hypotenuse | Tangent Function: tan(θ) = Opposite / Adjacent |
|---|
Which one is better sin cos or tan?
| Sine: soh sin(θ) = opposite / hypotenuse | Tangent: toa tan (θ) = opposite / adjacent |
|---|
What is the shortest side of a 30 60 90 triangle?
And because we know that we cut the base of the equilateral triangle in half, we can see that the side opposite the 30° angle (the shortest side) of each of our 30-60-90 triangles is exactly
half the length of the hypotenuse
.
How do you find sin given Cos?
All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out
Sin Theta = Cos (90 – Theta)
and Cos Theta = Sin (90 – Theta).
What is the formula of sin Cos?
In any right angled triangle, for any angle: The Sine of the Angle(sin A) =
the length of the opposite side / the length of the hypotenuse
. The Cosine of the Angle(cos A) = the length of the adjacent side / the length of the hypotenuse.
Is tangent sin over COS?
Each of these functions are derived in some way from sine and cosine. The tangent of x is defined to be its sine divided by its cosine:
tan x = sin x cos x
. … The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .
Why sine is called sine?
The word sine
originally came from the latin sinus, meaning “bay” or “inlet”
. … The earliest known reference to the sine function is from Aryabhata the Elder, who used both ardha-jya (half-chord) and jya (chord) to mean sine in Aryabhatiya, a Sanskrit text finished in 499 CE.
Why sin is used in Snell’s law?
Most people are familiar with Snell’s Law because of the apparent shortening of their legs that is observed when standing in water. … Snell’s Law states that
the ratio of the sine of the angles of incidence and transmission is equal to the ratio of the refractive index of the materials at the interface
.
Is sin vertical or horizontal?
The Sine and Cosine
This page contains a more detailed examination of the behavior of the sine (
vertical
component of the angle or ratio of opposite leg to hypotenuse) and cosine (horizontal component of the angle or ratio of adjacent leg to hypotenuse) functions.
Where is Cos equal to?
Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). The cosine is equal to
the adjacent side divided by the hypotenuse
(adj/hyp).
What is Sinx * COSX?
Answer : The expression for sin x + cos x in terms of sine is
sin x + sin (π / 2 – x)
. Let us see the detailed solution now. Explanation: Using pythagorean identity, Sin
2
x +Cos
2
x = 1.
Does sin a cos B?
Solution: If A and B are the acute angles of a right triangle,
sin A = cos B
.
How do you find a 30 60 90 Triangle?
- Short side (opposite the 30 degree angle) = x.
- Hypotenuse (opposite the 90 degree angle) = 2x.
- Long side (opposite the 60 degree angle) = x√3.
