Introduction to solve squared trigonometric functions:
There are the three basic trigonometric functions from which are the other three functions are derived. The square values of these functions are interrelated. All the trigonometric functions can be related to the squared functions of the other squared trigonometric functions. In the following article we will discuss in detail about the topic Solving Trigonometric Functions.
More about Solve Squared Trigonometric Functions.
The relations between the squared functions of the six trigonometric functions are,
`Si n^2 theta + cos^2 theta = 1`
`Cosec^2 theta - Cot^2 theta = 1`
`Sec^2 theta - Tan^2 theta = 1`
From these relations the values for the squared functions of the others can be derived as,
`Si n^2 theta = 1- Cos^2 theta`
`Cos^2 theta = 1- Si n^2 theta`
`Cosec^2 theta = 1+ Cot^2 theta`
`Cot^2 theta = Cosec^2 theta-1`
`Sec^2 theta = 1+ Tan^2 theta`
`Tan^2 theta = Sec^2 theta-1`
Also the basic relations between the squared trigonometric functions are,
`Si n^2 theta = 1/(cosec^2 theta)`
`Cos^2 theta = 1/(sec^2 theta)`
`Tan^2 theta = 1/(cot^2 theta)`
Using all these relations all the six trigonometric functions are related to each other.
Proof for the trigonometric relations:
In a right triangle let the opposite side = O, adjacent side = A, hypotenuse side = H. And `A^2 + O^2 = H^2` ,
`Si n theta = O /H`
`Cos theta = A/H`
`Tan theta = O /A`
`Si n^2 theta + cos^2 theta = O^2/H^2 + A^2/H^2 = (O^2+A^2)/H^2 = H^2/H^2 = 1`
`Cosec^2 theta - Cot^2 theta = H^2/O^2 - A^2/O^2 = (H^2 - A^2)/O^2 = O^2/O^2 = 1`
`Sec^2 theta - Tan^2 theta = H^2/A^2 - O^2/A^2 = (H^2 - O^2)/A^2 = A^2/A^2 = 1`
Between, if you have problem on these topics math formulas sheet, please browse expert math related websites for more help on Poisson Process.
Example Problem on Solve Squared Trigonometric Functions.
1. Solve `Tan^2 theta - Si n^2 theta` , using the squared trigonometric relations.
Solution:
`Tan^2 theta - Si n^2 theta`
`= (Si n^2 theta)/(Cos^2 theta) - Si n^2 theta`
`= Si n^2 theta (1/(Cos^2 theta) -1)`
`= Si n^2 theta (Sec^2 theta -1)`
`= Si n^2 theta (Tan^2 theta)`
There are the three basic trigonometric functions from which are the other three functions are derived. The square values of these functions are interrelated. All the trigonometric functions can be related to the squared functions of the other squared trigonometric functions. In the following article we will discuss in detail about the topic Solving Trigonometric Functions.
More about Solve Squared Trigonometric Functions.
The relations between the squared functions of the six trigonometric functions are,
`Si n^2 theta + cos^2 theta = 1`
`Cosec^2 theta - Cot^2 theta = 1`
`Sec^2 theta - Tan^2 theta = 1`
From these relations the values for the squared functions of the others can be derived as,
`Si n^2 theta = 1- Cos^2 theta`
`Cos^2 theta = 1- Si n^2 theta`
`Cosec^2 theta = 1+ Cot^2 theta`
`Cot^2 theta = Cosec^2 theta-1`
`Sec^2 theta = 1+ Tan^2 theta`
`Tan^2 theta = Sec^2 theta-1`
Also the basic relations between the squared trigonometric functions are,
`Si n^2 theta = 1/(cosec^2 theta)`
`Cos^2 theta = 1/(sec^2 theta)`
`Tan^2 theta = 1/(cot^2 theta)`
Using all these relations all the six trigonometric functions are related to each other.
Proof for the trigonometric relations:
In a right triangle let the opposite side = O, adjacent side = A, hypotenuse side = H. And `A^2 + O^2 = H^2` ,
`Si n theta = O /H`
`Cos theta = A/H`
`Tan theta = O /A`
`Si n^2 theta + cos^2 theta = O^2/H^2 + A^2/H^2 = (O^2+A^2)/H^2 = H^2/H^2 = 1`
`Cosec^2 theta - Cot^2 theta = H^2/O^2 - A^2/O^2 = (H^2 - A^2)/O^2 = O^2/O^2 = 1`
`Sec^2 theta - Tan^2 theta = H^2/A^2 - O^2/A^2 = (H^2 - O^2)/A^2 = A^2/A^2 = 1`
Between, if you have problem on these topics math formulas sheet, please browse expert math related websites for more help on Poisson Process.
Example Problem on Solve Squared Trigonometric Functions.
1. Solve `Tan^2 theta - Si n^2 theta` , using the squared trigonometric relations.
Solution:
`Tan^2 theta - Si n^2 theta`
`= (Si n^2 theta)/(Cos^2 theta) - Si n^2 theta`
`= Si n^2 theta (1/(Cos^2 theta) -1)`
`= Si n^2 theta (Sec^2 theta -1)`
`= Si n^2 theta (Tan^2 theta)`
No comments:
Post a Comment