Basic Trignometry Formulae Help

In summary, the formulas for function changes involving adding or subtracting pi/2 and 2pi are: sin (pi/2 - x) = sin x, cos (pi/2 - x) = -sin x, sin (2pi - x) = -cos x, and cos(x - pi/2) = sin x. It is important to be aware of the value inside the brackets, as it can affect the outcome of the function.
  • #1
utsav55
15
0

Homework Statement


Can you please list the formulae of function change while putting (pie/2 - x) and adding or subtracting 2Pie
Basicly, I need help on 2 formulae. One is add/subtract Pie/2 and the other is add/subtract 2Pie.

Homework Equations


sin (pie/2 - x) = sin x
cos (pie/2 - x) = - sin x

sin (2Pie - x) = -cos x

something like that... Its just example, may not be correct.

The Attempt at a Solution


I know a little something that All is +ve in first quadrant, only sin is +ve in 2nd quad, tan in 3rd and cos in 4th quad.
Maybe we can use this to determine +ve or -ve sin/cos when we add or subtract 2Pie or Pie.
 
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  • #2
2pi equals 360 degrees and pi/2 is 90 degrees. A sine and cosine function will be the same value if you add or take away 2pi as it is the same as adding or taking away 360 degrees and since the functions repeate every 360 degrees there will be no difference.
But be aware if the value inside the brackets goes lower than 0 your answer will be negative.

Taking away or adding pi/2 is simply changing a cos function into a sin function or vice versa. So cos(x- pi/2) = sinx

Since the sin and cosine functions are very similar, they are just offset by 90 degrees (pi/2) you are just swapping them round.
 
  • #3
please,send the formulae list of differentiation as well as integration on my email-id(sumit.anandd786@gmail.com).
 
  • #4
calum said:
But be aware if the value inside the brackets goes lower than 0 your answer will be negative.
This isn't true. For example, cos(x - 2pi) = cos(x), for all real values of x.
 

What are the basic trigonometry formulae?

The basic trigonometry formulae include sine, cosine, and tangent ratios which relate the sides of a right triangle to its angles. These are commonly used to solve for missing side lengths or angles in a triangle.

How do I remember the basic trigonometry formulae?

A common mnemonic device for remembering the basic trigonometry formulae is SOH-CAH-TOA, which stands for sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent.

Can the basic trigonometry formulae be applied to non-right triangles?

Yes, the basic trigonometry formulae can also be applied to non-right triangles using the Law of Sines and Law of Cosines. These formulas involve the ratios of all three sides and angles of a triangle.

What is the unit circle and how does it relate to the basic trigonometry formulae?

The unit circle is a circle with a radius of 1 centered at the origin on a coordinate plane. It is used to visualize the relationships between the trigonometric ratios and the coordinates of points on the circle. The x-coordinate corresponds to the cosine value and the y-coordinate corresponds to the sine value.

How can I use the basic trigonometry formulae in real life?

The basic trigonometry formulae have many real-life applications, such as in navigation, engineering, and architecture. They can be used to calculate distances, heights, and angles in various situations. For example, trigonometry is used in surveying to measure the angles and distances between points on land.

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