sin(-98 degrees) to a positive acute angle

To find \( \sin(-98^\circ) \) as a positive acute angle, let's go through the steps:

1. **Convert to Positive Angle**: First, rewrite \(-98^\circ\) as a positive angle by adding \(360^\circ\):
   \[
   -98^\circ + 360^\circ = 262^\circ
   \]

2. **Reference Angle**: Now, find the reference angle for \(262^\circ\). This angle is in the third quadrant, where we subtract \(180^\circ\):
   \[
   262^\circ - 180^\circ = 82^\circ
   \]

3. **Sin of Reference Angle**: Since sine is negative in the third quadrant, we know that:
   \[
   \sin(262^\circ) = -\sin(82^\circ)
   \]

4. **Final Answer in Terms of Positive Acute Angle**: Thus,
   \[
   \sin(-98^\circ) = -\sin(82^\circ)
   \]

So, the equivalent positive acute angle is **82 degrees**.

Would you like further details, or do you have any questions? 

Here are some additional practice questions related to this concept:

1. Find \(\sin(-120^\circ)\) as a positive acute angle.
2. Convert \(\cos(-215^\circ)\) to a positive acute angle.
3. Express \(\tan(250^\circ)\) as a positive acute angle.
4. Find the positive acute angle equivalent for \(\sin(-45^\circ)\).
5. Determine the reference angle for \(\cos(-320^\circ)\).

**Tip:** To find the reference angle, always use the smallest angle formed between the terminal side of the given angle and the x-axis.

Discover how to express sin(-98°) as a positive acute angle. This guide explains key trigonometric concepts, including converting negative angles, identifying reference angles, and determining sine values based on quadrants. Ideal for students in Grades 10-12.

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