What is the exact value of sin Pi 2?
Trig Values on the unit circle
| A | B |
|---|---|
| sin pi/2 | 1 |
| cos 2pi/3 | -1/2 |
| cos 3pi/4 | -sqroot2/2 |
| cos 5pi/6 | -sqroot 3/2 |
Which coordinate is equal to Sin Pi 2?
Sine (theta+pi/2) is equal to cosine.
Where is pi over 2 on the unit circle?
2 Answers. The interval (−π2,π2) is the right half of the unit circle.
Why can sine and cosine never be greater than 1 1?
Note: Since the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse, the values will never be more than 1, because (some number) / (a bigger number) from a right triangle is always going to be smaller than 1.
Why is sin less than 1?
the value of sin and Cos is always less than 1 because sin is equals two perpendicular ÷ hypotenuse and perpendicular is always smaller than hypotenuse so it is not possible that sin is greater than 1 same case in cos also cos is equals to base divided by hypotenuse and base is always smaller than hypotenuse so it is …
Why is tan greater than 1?
There is no such restriction on the length of a and b, so their ratio (which we call the tangent) can get any value. Because in a triangle with one right angle, the diagonal c is always longer than the two others a and b, making the ratios a/c and b/c (which we call sine and cosine) both smaller than 1.
Can a sine ratio be greater than 1?
A = 1 is if a = c, but that would make for a strange triangle!), the sine ratio cannot be greater than 1.
Is the hypotenuse the longest side?
In a right triangle, the hypotenuse is the longest side, an “opposite” side is the one across from a given angle, and an “adjacent” side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.
Can the cosine ratio be greater than 1?
The sine and cosine ratios of an angle cannot be greater than 1. The tangent ratio has no such restriction.
What is ratio for Cosine?
Cosine ratios are specifically the ratio of the side adjacent to the represented base angle over the hypotenuse. Sine, cosine tangent where sine is the ratio of the opposite side to the hypotenuse, cosine is ratio of adjacent side to hypotenuse and tangent is ratio of opposite side to adjacent.
How do you find cosine of an angle?
Sin, Cos and Tan
- The sine of the angle = the length of the opposite side. the length of the hypotenuse.
- The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
- The tangent of the angle = the length of the opposite side. the length of the adjacent side.
What is tan ratio?
The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. tangent=length of the leg opposite to the anglelength of the leg adjacent to the angle abbreviated as “tan” Example: In the triangle shown, tan(A)=68 or 34 and tan(B)=86 or 43 .
What are the 3 trigonometric ratios?
There are three basic trigonometric ratios: sine , cosine , and tangent . Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non- 90° angles.
How do you calculate tan?
In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). In a formula, it is written simply as ‘tan’.
What is sin θ?
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 . No matter the size of the triangle, the values of sin(θ) and cos(θ) are the same for a given θ, as illustrated below.
What is sin 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). (1) Memorize: sine = (opposite side) / hypotenuse. cosine = (adjacent side) / hypotenuse.
Why do we use sine?
The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. Example: To find the length of the side opposite the angle, d, we use the sine function.
Who invented sine?
Abu’l Wafa
What is the value of sine?
As can be seen from the figure, sine has a value of 0 at 0° and a value of 1 at 90°. Cosine follows the opposite pattern; this is because sine and cosine are cofunctions (described later). The other commonly used angles are 30° ( ), 45° ( ), 60° ( ) and their respective multiples.
What is the sine value of 5 pi over 3?
The angle 5pi/3 is in the fourth quadrant (meaning cosine is positive while sine & tangent are negative), and its reference angle is 60 degrees with respect to the horizontal. Therefore its sine is -sqrt(3)/2, its cosine is 1/2, and its tangent is -sqrt(3).
Does sine have a unit?
The trig functions evaluate differently depending on the units on q. For example, sin(90°) = 1, while sin(90)=0.89399…. If there is no unit after the angle, the trig function evaluates its parameter as a radian measurement.
Do you use radians or degrees in physics?
In particular, rotational motion equations are almost always expressed using radians. The initial parameters of a problem might be in degrees, but you should convert these angles to radians before using them. You should use degrees when you are measuring angles using a protractor, or describing a physical picture.
Are angles dimensionless?
Angles measured in radians are considered to be dimensionless because the radian measure of angles is defined as the ratio of two lengths θ=sr (where s is some arc measuring s-units in length, and r is the radius) however the degree measure is not defined in this way and it is said to be dimensionless too.
Is Pi a dimensionless quantity?
All pure numbers are dimensionless quantities, for example 1, i, π, e, and φ. Units of number such as the dozen, gross, googol, and Avogadro’s number may also be considered dimensionless.
Are radians dimensionless?
Although the radian is a unit of measure, it is a dimensionless quantity. This can be seen from the definition given earlier: the angle subtended at the centre of a circle, measured in radians, is equal to the ratio of the length of the enclosed arc to the length of the circle’s radius.
Why Radian and steradian is dimensionless?
The name is derived from the Greek στερεός stereos ‘solid’ + radian. The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the center. Both the numerator and denominator of this ratio have dimension length squared (i.e. L2/L2 = 1, dimensionless).