list the possible valures of sin a if a is a quadrental angle
Wow, after 45 years of teaching math I just learned something new.
I had never heard of a quadrantal angle, had to look it up
http://www.mathwords.com/q/quadrantal_angle.htm
take the sign of each of those angles and see what you get.
To determine the possible values of sine (sin) for an angle depending on its quadrant, you can follow these steps:
1. Identify the quadrant of the angle: Quadrantal angles lie on the axes and have specific characteristics in each quadrant.
- In the first quadrant (0° < a < 90°), all three trigonometric functions (sine, cosine, and tangent) are positive.
- In the second quadrant (90° < a < 180°), only sine is positive.
- In the third quadrant (180° < a < 270°), only tangent is positive.
- In the fourth quadrant (270° < a < 360°), only cosine is positive.
2. Determine the values of sine within the given quadrant:
- In the first quadrant, since all three trigonometric functions are positive, sin a could be any positive value within the range of 0 to 1.
- In the second quadrant, only sine is positive, so sin a can vary between 0 and 1.
- In the third and fourth quadrants, where sine is negative, sin a can range from -1 to 0.
In summary:
- First quadrant: 0 < sin a < 1 (positive values)
- Second quadrant: 0 < sin a < 1 (positive values)
- Third and fourth quadrants: -1 < sin a < 0 (negative values)