JEE Exam > JEE Questions > sin (200)0+ cos (200)0 isa)Zerob)Positivec)Ze...
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sin (200)0 + cos (200)0 is
- a)Zero
- b)Positive
- c)Zero or positive.
- d)Negative
Correct answer is option 'D'. Can you explain this answer?
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sin (200)0+ cos (200)0 isa)Zerob)Positivec)Zero or positive.d)Negative...
Because both sin 2000 and cos 2000 lies in 3rd quadrant. In 3rd quadrant values of sin and cos are negative.
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sin (200)0+ cos (200)0 isa)Zerob)Positivec)Zero or positive.d)Negative...
To determine the sign of sin(200)0 and cos(200)0, we need to recall the unit circle and the values of sine and cosine for angles in the different quadrants.
The unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on a coordinate plane. It helps us understand the relationship between angles and the coordinates on the circle.
The circle is divided into four quadrants: Quadrant I (0°-90°), Quadrant II (90°-180°), Quadrant III (180°-270°), and Quadrant IV (270°-360°).
In Quadrant I, both the x-coordinate (cosine) and the y-coordinate (sine) are positive. In Quadrant II, the x-coordinate (cosine) is negative, but the y-coordinate (sine) is positive. In Quadrant III, both the x-coordinate (cosine) and the y-coordinate (sine) are negative. In Quadrant IV, the x-coordinate (cosine) is positive, but the y-coordinate (sine) is negative.
Now let's consider the given angle, 200°.
Since 200° is greater than 180°, it lies in Quadrant III.
- The cosine of 200° will be negative because it is in Quadrant III.
- The sine of 200° will also be negative because it is in Quadrant III.
Hence, sin(200)0 and cos(200)0 are both negative.
Therefore, the correct answer is option 'D' - Negative.
The unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on a coordinate plane. It helps us understand the relationship between angles and the coordinates on the circle.
The circle is divided into four quadrants: Quadrant I (0°-90°), Quadrant II (90°-180°), Quadrant III (180°-270°), and Quadrant IV (270°-360°).
In Quadrant I, both the x-coordinate (cosine) and the y-coordinate (sine) are positive. In Quadrant II, the x-coordinate (cosine) is negative, but the y-coordinate (sine) is positive. In Quadrant III, both the x-coordinate (cosine) and the y-coordinate (sine) are negative. In Quadrant IV, the x-coordinate (cosine) is positive, but the y-coordinate (sine) is negative.
Now let's consider the given angle, 200°.
Since 200° is greater than 180°, it lies in Quadrant III.
- The cosine of 200° will be negative because it is in Quadrant III.
- The sine of 200° will also be negative because it is in Quadrant III.
Hence, sin(200)0 and cos(200)0 are both negative.
Therefore, the correct answer is option 'D' - Negative.
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sin (200)0+ cos (200)0 isa)Zerob)Positivec)Zero or positive.d)NegativeCorrect answer is option 'D'. Can you explain this answer?
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