Signs of the trigonometric functions of the angle -200

In summary, when determining the signs of trigonometric functions for an angle in standard position, we can use the mnemonic device "All Students Take Calculus" to remember which quadrants result in positive or negative values. For the angle -200°, the signs of the trigonometric functions are as follows: sin(-200°) and csc(-200°) are both positive, while cos(-200°), tan(-200°), sec(-200°), and cot(-200°) are all negative.
  • #1
MattO7766
2
0
Determine the signs of the trigonometric functions of the angle -200° in standard position.

sin(-200°)
cos(-200°)
tan(-200°)
csc(-200°)
sec(-200°)
cot(-200°)

Information:
Q1= (All Positive)
Q2= (sin csc)
Q3= (tan cot)
Q4= (cos sec)

Answer:
sin(-200°) = Positive
cos(-200°) = Negative
tan(-200°) = Negative
csc(-200°) = Positive
sec(-200°) = Negative
cot(-200°) = Negative

Could someone please help me with this, I'm very confused
 
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  • #2
http://planetmath.org/DeterminingSignsOfTrigonometricFunctions.html

Since -200° lies in the second quadrant, then all are positive except for SIN and CSC, as described in the link above. Use the mnemonic device "All Students Take Calculus" as suggested and you will get any question relating to this task 100% on an exam!
 

1. What are the signs of the trigonometric functions of the angle -200?

The signs of the trigonometric functions for an angle of -200 degrees are as follows:

  • Sine: negative
  • Cosine: positive
  • Tangent: negative
  • Cosecant: negative
  • Secant: positive
  • Cotangent: negative

2. Why is the sign of sine negative for an angle of -200 degrees?

The sign of sine is negative for an angle of -200 degrees because the sine function is negative in the third quadrant, which is where -200 degrees falls on the unit circle. In this quadrant, the y-coordinate (sine) is negative and the x-coordinate (cosine) is positive.

3. What does the sign of cosine being positive for an angle of -200 degrees indicate?

The positive sign of cosine for an angle of -200 degrees indicates that the cosine function is positive in the fourth quadrant, which is where -200 degrees falls on the unit circle. In this quadrant, both the x-coordinate (cosine) and y-coordinate (sine) are positive.

4. How can the sign of tangent be negative for an angle of -200 degrees?

The sign of tangent is negative for an angle of -200 degrees because the tangent function is negative in the second quadrant, which is where -200 degrees falls on the unit circle. In this quadrant, the y-coordinate (sine) is positive and the x-coordinate (cosine) is negative.

5. Is it possible for the signs of cosecant, secant, and cotangent to be different for an angle of -200 degrees?

Yes, it is possible for the signs of cosecant, secant, and cotangent to be different for an angle of -200 degrees. This is because these functions are reciprocals of sine, cosine, and tangent, respectively. Therefore, their signs will be the inverse of the corresponding trigonometric function's sign. For example, the cosecant of -200 degrees will be positive because its reciprocal, the sine function, is negative in the third quadrant.

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