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If p = sin (989o) cos (991o), then which one of the following is correct?
- a)p is finite and positive
- b)p is finite and negative
- c)p = 0
- d)p is undefined
Correct answer is option 'B'. Can you explain this answer?
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If p = sin (989o) cos (991o), then which one of the following is corre...
Solution:
Given, p = sin(989°) cos(991°)
We know that sinθ and cosθ are periodic functions with a period of 360°.
Hence, we can write sin(989°) as sin(989°- 720°) = sin(269°)
Similarly, cos(991°) can be written as cos(991°-720°) = cos(271°)
Now, p = sin(269°) cos(271°)
Using the identity sin(A+B) = sinA cosB + cosA sinB, we get
p = (sin(269°+271°))/2
= (sin(540°))/2
= (sin180°)/2
= 0
Therefore, p = 0.
Hence, the correct option is (c) p = 0.
Note: The given answer (B) is incorrect.
Given, p = sin(989°) cos(991°)
We know that sinθ and cosθ are periodic functions with a period of 360°.
Hence, we can write sin(989°) as sin(989°- 720°) = sin(269°)
Similarly, cos(991°) can be written as cos(991°-720°) = cos(271°)
Now, p = sin(269°) cos(271°)
Using the identity sin(A+B) = sinA cosB + cosA sinB, we get
p = (sin(269°+271°))/2
= (sin(540°))/2
= (sin180°)/2
= 0
Therefore, p = 0.
Hence, the correct option is (c) p = 0.
Note: The given answer (B) is incorrect.
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