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The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations is
- a)nπ + (7π/4)
- b)nπ - (7π/4)
- c)2nπ + (7π/4)
- d)2nπ - (7π/4)
Correct answer is option 'C'. Can you explain this answer?
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The general value of θ which satisfies tanθ=-1 and cos&the...
Given Information:
- tanθ = -1
- cosθ = 1/√2
Solution:
Finding the value of θ for tanθ = -1:
- We know that tanθ = -1 in the second and fourth quadrants.
- In the second quadrant, tanθ is negative and equal to 1.
- Therefore, θ = (3π)/4 in the second quadrant.
- In the fourth quadrant, tanθ is negative and equal to -1.
- Therefore, θ = (7π)/4 in the fourth quadrant.
Finding the value of θ for cosθ = 1/√2:
- We know that cosθ = 1/√2 in the first and fourth quadrants.
- In the first quadrant, cosθ is positive and equal to 1/√2.
- Therefore, θ = π/4 in the first quadrant.
- In the fourth quadrant, cosθ is positive and equal to 1/√2.
- Therefore, θ = (7π)/4 in the fourth quadrant.
Combining the values of θ:
- From the above analysis, we see that θ = (7π)/4 satisfies both tanθ = -1 and cosθ = 1/√2.
- The general value of θ that satisfies these equations is given by θ = 2nπ + (7π)/4, where n is an integer.
- Therefore, the correct answer is option 'C': 2nπ + (7π)/4.
- tanθ = -1
- cosθ = 1/√2
Solution:
Finding the value of θ for tanθ = -1:
- We know that tanθ = -1 in the second and fourth quadrants.
- In the second quadrant, tanθ is negative and equal to 1.
- Therefore, θ = (3π)/4 in the second quadrant.
- In the fourth quadrant, tanθ is negative and equal to -1.
- Therefore, θ = (7π)/4 in the fourth quadrant.
Finding the value of θ for cosθ = 1/√2:
- We know that cosθ = 1/√2 in the first and fourth quadrants.
- In the first quadrant, cosθ is positive and equal to 1/√2.
- Therefore, θ = π/4 in the first quadrant.
- In the fourth quadrant, cosθ is positive and equal to 1/√2.
- Therefore, θ = (7π)/4 in the fourth quadrant.
Combining the values of θ:
- From the above analysis, we see that θ = (7π)/4 satisfies both tanθ = -1 and cosθ = 1/√2.
- The general value of θ that satisfies these equations is given by θ = 2nπ + (7π)/4, where n is an integer.
- Therefore, the correct answer is option 'C': 2nπ + (7π)/4.
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The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations isa)nπ + (7π/4)b)nπ - (7π/4)c)2nπ + (7π/4)d)2nπ - (7π/4)Correct answer is option 'C'. Can you explain this answer?
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The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations isa)nπ + (7π/4)b)nπ - (7π/4)c)2nπ + (7π/4)d)2nπ - (7π/4)Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations isa)nπ + (7π/4)b)nπ - (7π/4)c)2nπ + (7π/4)d)2nπ - (7π/4)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations isa)nπ + (7π/4)b)nπ - (7π/4)c)2nπ + (7π/4)d)2nπ - (7π/4)Correct answer is option 'C'. Can you explain this answer?.
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