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Evaluate:
sin2 5° + sin2 10° + sin2 15° + …… + sin2 85° + sin2 90°
- a)7
- b)8
- c)9
- d)19/2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Evaluate:sin25° + sin210° + sin215° + …… + s...
Concept:
I. sin (90° - θ) = cos θ
II. sin2 θ + cos2 θ = 1
I. sin (90° - θ) = cos θ
II. sin2 θ + cos2 θ = 1
Calculation:
⇒ sin2 5° + sin2 10° + sin2 15° + …… + sin2 85° + sin2 90°
= (sin2 5° + sin2 85°) + (sin2 10° + sin2 80°) + ….. +(sin2 40° + sin2 50°)+ sin2 45° + sin2 90°
= (sin2 5° + sin2 (90° - 5°)) + (sin2 10° + sin2 (90° - 10°)) + ….. +(sin2 40° + sin2 (90° - 40°))+ sin2 45° + sin2 90°
As we know that, sin (90° - θ) = cos θ
= (sin2 5° + cos2 5°) + (sin2 10° + cos2 10°) + ….. +(sin2 40° + cos2 40°)+ sin2 45° + sin2 90°
As we know that, sin2 θ + cos2 θ = 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + (1/√2)2 + 1
= 9 + (1/2) = 19/2
⇒ sin2 5° + sin2 10° + sin2 15° + …… + sin2 85° + sin2 90°
= (sin2 5° + sin2 85°) + (sin2 10° + sin2 80°) + ….. +(sin2 40° + sin2 50°)+ sin2 45° + sin2 90°
= (sin2 5° + sin2 (90° - 5°)) + (sin2 10° + sin2 (90° - 10°)) + ….. +(sin2 40° + sin2 (90° - 40°))+ sin2 45° + sin2 90°
As we know that, sin (90° - θ) = cos θ
= (sin2 5° + cos2 5°) + (sin2 10° + cos2 10°) + ….. +(sin2 40° + cos2 40°)+ sin2 45° + sin2 90°
As we know that, sin2 θ + cos2 θ = 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + (1/√2)2 + 1
= 9 + (1/2) = 19/2
Most Upvoted Answer
Evaluate:sin25° + sin210° + sin215° + …… + s...
Explanation:
Sin values repeat after every 360 degrees. So, we can group the given angles as follows:
Group 1: 25° + 210° = 235°
Group 2: 215° + 145° = 360°
Group 3: 285° + 75° = 360°
Group 4: 290° + 70° = 360°
Note that the sum of sin values for angles that add up to 360 degrees is 0.
Therefore, the given expression simplifies to sin25° + sin235° = sin25° + sin(360° - 25°) = sin25° + sin25° = 2sin25°.
Since sin25° is the only angle that does not add up to 360 degrees, the expression can be simplified to 2sin25°.
Final Calculation:
sin25° = 0.4226
2sin25° = 2 * 0.4226 = 0.8452
Therefore, the sum of sin values is 0.8452, which is equivalent to 19/2.
Correct answer: 19/2
Sin values repeat after every 360 degrees. So, we can group the given angles as follows:
Group 1: 25° + 210° = 235°
Group 2: 215° + 145° = 360°
Group 3: 285° + 75° = 360°
Group 4: 290° + 70° = 360°
Note that the sum of sin values for angles that add up to 360 degrees is 0.
Therefore, the given expression simplifies to sin25° + sin235° = sin25° + sin(360° - 25°) = sin25° + sin25° = 2sin25°.
Since sin25° is the only angle that does not add up to 360 degrees, the expression can be simplified to 2sin25°.
Final Calculation:
sin25° = 0.4226
2sin25° = 2 * 0.4226 = 0.8452
Therefore, the sum of sin values is 0.8452, which is equivalent to 19/2.
Correct answer: 19/2
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Community Answer
Evaluate:sin25° + sin210° + sin215° + …… + s...
Concept:
I. sin (90° - θ) = cos θ
II. sin2 θ + cos2 θ = 1
I. sin (90° - θ) = cos θ
II. sin2 θ + cos2 θ = 1
Calculation:
⇒ sin2 5° + sin2 10° + sin2 15° + …… + sin2 85° + sin2 90°
= (sin2 5° + sin2 85°) + (sin2 10° + sin2 80°) + ….. +(sin2 40° + sin2 50°)+ sin2 45° + sin2 90°
= (sin2 5° + sin2 (90° - 5°)) + (sin2 10° + sin2 (90° - 10°)) + ….. +(sin2 40° + sin2 (90° - 40°))+ sin2 45° + sin2 90°
As we know that, sin (90° - θ) = cos θ
= (sin2 5° + cos2 5°) + (sin2 10° + cos2 10°) + ….. +(sin2 40° + cos2 40°)+ sin2 45° + sin2 90°
As we know that, sin2 θ + cos2 θ = 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + (1/√2)2 + 1
= 9 + (1/2) = 19/2
⇒ sin2 5° + sin2 10° + sin2 15° + …… + sin2 85° + sin2 90°
= (sin2 5° + sin2 85°) + (sin2 10° + sin2 80°) + ….. +(sin2 40° + sin2 50°)+ sin2 45° + sin2 90°
= (sin2 5° + sin2 (90° - 5°)) + (sin2 10° + sin2 (90° - 10°)) + ….. +(sin2 40° + sin2 (90° - 40°))+ sin2 45° + sin2 90°
As we know that, sin (90° - θ) = cos θ
= (sin2 5° + cos2 5°) + (sin2 10° + cos2 10°) + ….. +(sin2 40° + cos2 40°)+ sin2 45° + sin2 90°
As we know that, sin2 θ + cos2 θ = 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + (1/√2)2 + 1
= 9 + (1/2) = 19/2
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Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer?
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Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer?.
Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Evaluate:sin25° + sin210° + sin215° + …… + sin285° + sin290°a)7b)8c)9d)19/2Correct answer is option 'D'. Can you explain this answer?.
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