Tuesday, July 6, 2010

Trignometric Equations

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An equation connecting trigonometric ratios of an angle is called a Trigonometric Identity.
An equation that gives the relation between lines and angles of a right triangle is called a Trigonometric Equation. It should be noted that an equation is satisfied for particular values of the variable whereas an identity is true for all values of the variable.

The table below gives the values of all the trigonometric ratios for different values of θ.

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θ T. ratios
30°
45°
60°
90°
Sin θ
0
1/2
1/√2
√3/2
1
Cos θ
1
√3/2
1/√2
1/2
0
Tan θ
0
1/√3
1
√3
Not Defined
Cosec θ
Not Defined
2
√2
2/√3
1
Sec θ
1
2/√3
√2
2
Not Defined
Cot θ
Not Defined
√3
1
1/√3
0

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Listed below are some steps that help in determining whether an equation is Identity or not.

Step 1:- Replace the variable of the given equation by 0°, 30°, 45°, 60°, and 90° one by one.
Step 2:- If the LHS of the given equation is not equal to its RHS for some values of θ mentioned in step 1, then it is not an identity.

If all values of the variable mentioned in step 1 satisfy the given equation, then simplify the LHS and RHS of the given equation to see whether the two sides are equal or not. If the two sides are equal, the equation is an identity.















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