To express sin(-200°) as a function of a positive acute angle in two different forms, we can use the properties of trigonometric functions. Here's how you can approach this problem step by step:
1. First, note that sin(-200°) is equivalent to sin(160°) because the sine function has a period of 360°, meaning that sin(x) = sin(x + 360°) for any angle x.
2. To express sin(160°) in terms of a positive acute angle, we need to find a reference angle in the first quadrant that has the same sine value. The reference angle for 160° is 20° because sin(20°) = sin(180° - 20°) = sin(160°).
3. Since sin is positive in both the first and second quadrants, sin(160°) = sin(20°) = sin(180° - 20°). Therefore, sin(160°) can be expressed as sin(20°) in terms of a positive acute angle.
4. Another way to express sin(160°) as a function of a positive acute angle is to consider the periodicity of the sine function. Since sin(160°) = sin(180° - 20°), we can also write sin(160°) as sin(180° + 20°) = sin(200°).
In conclusion, sin(-200°) can be expressed as sin(20°) and sin(200°) as functions of a positive acute angle. These two forms provide different ways to represent sin(-200°) using trigonometric properties and periodicity.
