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If cosec theta equal to root 10 then find the values of tan theta and secant theta?
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If cosec theta equal to root 10 then find the values of tan theta and ...
Given Information
If cosec theta = √10, then we can derive other trigonometric values based on this information.
Understanding Cosecant
- Cosecant is the reciprocal of sine:
cosec θ = 1/sin θ
- Therefore, if cosec θ = √10, we can express this as:
sin θ = 1/√10
Finding the Value of Cosine
To find cos θ, we will use the Pythagorean identity:
- sin² θ + cos² θ = 1
Substituting the value of sin θ:
- (1/√10)² + cos² θ = 1
This simplifies to:
- 1/10 + cos² θ = 1
Rearranging gives us:
- cos² θ = 1 - 1/10 = 9/10
Thus:
- cos θ = √(9/10) = 3/√10
Calculating Secant
Secant is the reciprocal of cosine:
- sec θ = 1/cos θ
Substituting the value of cos θ:
- sec θ = √10/3
Finding the Value of Tangent
Tangent is the ratio of sine to cosine:
- tan θ = sin θ/cos θ
Substituting the values we found:
- tan θ = (1/√10)/(3/√10) = 1/3
Final Values
- tan θ = 1/3
- sec θ = √10/3
These values can now be used for further calculations or applications in trigonometry.
If cosec theta = √10, then we can derive other trigonometric values based on this information.
Understanding Cosecant
- Cosecant is the reciprocal of sine:
cosec θ = 1/sin θ
- Therefore, if cosec θ = √10, we can express this as:
sin θ = 1/√10
Finding the Value of Cosine
To find cos θ, we will use the Pythagorean identity:
- sin² θ + cos² θ = 1
Substituting the value of sin θ:
- (1/√10)² + cos² θ = 1
This simplifies to:
- 1/10 + cos² θ = 1
Rearranging gives us:
- cos² θ = 1 - 1/10 = 9/10
Thus:
- cos θ = √(9/10) = 3/√10
Calculating Secant
Secant is the reciprocal of cosine:
- sec θ = 1/cos θ
Substituting the value of cos θ:
- sec θ = √10/3
Finding the Value of Tangent
Tangent is the ratio of sine to cosine:
- tan θ = sin θ/cos θ
Substituting the values we found:
- tan θ = (1/√10)/(3/√10) = 1/3
Final Values
- tan θ = 1/3
- sec θ = √10/3
These values can now be used for further calculations or applications in trigonometry.
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If cosec theta equal to root 10 then find the values of tan theta and secant theta?
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If cosec theta equal to root 10 then find the values of tan theta and secant theta? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If cosec theta equal to root 10 then find the values of tan theta and secant theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosec theta equal to root 10 then find the values of tan theta and secant theta?.
If cosec theta equal to root 10 then find the values of tan theta and secant theta? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If cosec theta equal to root 10 then find the values of tan theta and secant theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosec theta equal to root 10 then find the values of tan theta and secant theta?.
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