In the previous post we have discussed about How to Solve Median Worksheets and In today's session we are going to discuss about Trigonometric Equations. Hello students, in this section we are going to discuss the Trigonometric equations. An equation that denotes trigonometric functions is a trigonometric equation.
For example: Cos q = ½.
When we solve trigonometric equations using different relations then the equation is converted to form through which value of other variable can be obtained. The roots of trigonometric function are obtained by the inverse trigonometric functions.
Suppose we have sin q + sin 2q + sin 3q = 0;
This trigonometric equation can be reduced to form 2 sin 2q cos q + sin 2q = 0;
Or we can also write as:
Sin 2q (2 cos q + 1) = 0;
When we solve this equation we get the value of sin 2q as 0;
Sin 2q (2 cos q + 1) = 0;
Sin 2q = 0;
And the value of cos is:
2 cos q + 1 = 0;
2 cos q = -1;
Cos q = -1/2;
So the value of cos q is -1/2.This equation result gives the result of the trigonometric equations.
So q = ½ arcsin 0 = n ⊼/2;
q = arcos (-1/2);
q = 2/3 ⊼(3n +½);
Here, the value of ‘n’ may be positive or negative integer. (know more about Trigonometric Equations, here).
Now we will see how to solve the trigonometric equations.
Assumes we have the trigonometric equation 4 tan3 q – tan q = 0, which lies in the interval [0, 2⊼]. Then we can solve this as shown below:
So the given trigonometric equation is: 4 tan3 q – tan q = 0;
We can write the equation as:
=> 4 tan3 q – tan q = 0;
=> Tan q (4 tan2 q – 1) = 0;
So the value of tan ‘q’ is 0;
Or tan q = +1/√3. For every value of q ∈[0, 2⊼],
Tan q = 0;
It means the value of ‘q’ is 0, ⊼or 2⊼.
While
Tan q = 1/√3,
q = ⊼/ 6 or 7⊼/ 6,
Tan q = -1/√3,
q = 5⊼/ 6 or 11⊼/ 6.
The answer of what is a quadrilateral is that, quadrilateral is a type of polygon that have four sides and this can be many types like rectangle, square and many more. class 12 cbse sample papers has all the advanced and core topic so that every students can aware from them.
For example: Cos q = ½.
When we solve trigonometric equations using different relations then the equation is converted to form through which value of other variable can be obtained. The roots of trigonometric function are obtained by the inverse trigonometric functions.
Suppose we have sin q + sin 2q + sin 3q = 0;
This trigonometric equation can be reduced to form 2 sin 2q cos q + sin 2q = 0;
Or we can also write as:
Sin 2q (2 cos q + 1) = 0;
When we solve this equation we get the value of sin 2q as 0;
Sin 2q (2 cos q + 1) = 0;
Sin 2q = 0;
And the value of cos is:
2 cos q + 1 = 0;
2 cos q = -1;
Cos q = -1/2;
So the value of cos q is -1/2.This equation result gives the result of the trigonometric equations.
So q = ½ arcsin 0 = n ⊼/2;
q = arcos (-1/2);
q = 2/3 ⊼(3n +½);
Here, the value of ‘n’ may be positive or negative integer. (know more about Trigonometric Equations, here).
Assumes we have the trigonometric equation 4 tan3 q – tan q = 0, which lies in the interval [0, 2⊼]. Then we can solve this as shown below:
So the given trigonometric equation is: 4 tan3 q – tan q = 0;
We can write the equation as:
=> 4 tan3 q – tan q = 0;
=> Tan q (4 tan2 q – 1) = 0;
So the value of tan ‘q’ is 0;
Or tan q = +1/√3. For every value of q ∈[0, 2⊼],
Tan q = 0;
It means the value of ‘q’ is 0, ⊼or 2⊼.
While
Tan q = 1/√3,
q = ⊼/ 6 or 7⊼/ 6,
Tan q = -1/√3,
q = 5⊼/ 6 or 11⊼/ 6.
The answer of what is a quadrilateral is that, quadrilateral is a type of polygon that have four sides and this can be many types like rectangle, square and many more. class 12 cbse sample papers has all the advanced and core topic so that every students can aware from them.
No comments:
Post a Comment