Evaluate The Expression Below, Expressing Your Answer In Degrees.$-250^{\circ} + 2 \arcsin (1$\]

Introduction

In this article, we will evaluate the given expression $-250^{\circ} + 2 \arcsin (1)$ and express our answer in degrees. The expression involves the use of trigonometric functions, specifically the arcsine function, and we will need to apply various mathematical concepts to simplify and evaluate it.

Understanding the Arcsine Function

The arcsine function, denoted by $\arcsin x$, is the inverse of the sine function. It returns the angle whose sine is a given value. In other words, if $\sin \theta = x$, then $\arcsin x = \theta$. The range of the arcsine function is typically restricted to the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$ to ensure that the function is one-to-one.

Evaluating the Arcsine Function

In the given expression, we have $\arcsin (1)$. Since the sine of $\frac{\pi}{2}$ is 1, we can conclude that $\arcsin (1) = \frac{\pi}{2}$. Therefore, the expression becomes $-250^{\circ} + 2 \cdot \frac{\pi}{2}$.

Converting Radians to Degrees

To express our answer in degrees, we need to convert the value of $\frac{\pi}{2}$ from radians to degrees. We know that $\pi$ radians is equivalent to $180^{\circ}$, so $\frac{\pi}{2}$ radians is equivalent to $90^{\circ}$.

Simplifying the Expression

Now that we have converted the value of $\frac{\pi}{2}$ to degrees, we can simplify the expression. We have $-250^{\circ} + 2 \cdot 90^{\circ}$. Using the distributive property, we can rewrite this as $-250^{\circ} + 180^{\circ} + 180^{\circ}$.

Evaluating the Expression

Finally, we can evaluate the expression by adding the values. We have $-250^{\circ} + 180^{\circ} + 180^{\circ} = -250^{\circ} + 360^{\circ}$.

Simplifying the Final Expression

To simplify the final expression, we can use the fact that adding or subtracting a multiple of $360^{\circ}$ does not change the value of the angle. Therefore, we can rewrite the expression as $-250^{\circ} + 360^{\circ} = 110^{\circ}$.

Conclusion

In this article, we evaluated the expression $-250^{\circ} + 2 \arcsin (1)$ and expressed our answer in degrees. We applied various mathematical concepts, including the use of the arcsine function and the conversion of radians to degrees. Our final answer is $110^{\circ}$.

Frequently Asked Questions

• Q: What is the arcsine function? A: The arcsine function is the inverse of the sine function. It returns the angle whose sine is a given value.
• Q: How do you evaluate the expression $-250^{\circ} + 2 \arcsin (1)$? A: To evaluate the expression, we need to apply various mathematical concepts, including the use of the arcsine function and the conversion of radians to degrees.
• Q: What is the final answer to the expression $-250^{\circ} + 2 \arcsin (1)$? A: The final answer to the expression is $110^{\circ}$.

References

• [1] "Trigonometry" by Michael Corral, 2015.
• [2] "Calculus" by Michael Spivak, 2008.
• [3] "Mathematics for Computer Science" by Eric Lehman, 2018.

Further Reading

• For more information on the arcsine function, see [1].
• For more information on the conversion of radians to degrees, see [2].
• For more information on mathematical concepts, see [3].
  

Introduction

In our previous article, we evaluated the expression $-250^{\circ} + 2 \arcsin (1)$ and expressed our answer in degrees. In this article, we will answer some frequently asked questions related to the expression and provide additional information to help readers understand the concept better.

Q&A

Q: What is the arcsine function and how is it used in the expression?

A: The arcsine function is the inverse of the sine function. It returns the angle whose sine is a given value. In the expression $-250^{\circ} + 2 \arcsin (1)$, the arcsine function is used to find the angle whose sine is 1.

Q: How do you evaluate the expression $-250^{\circ} + 2 \arcsin (1)$?

A: To evaluate the expression, we need to apply various mathematical concepts, including the use of the arcsine function and the conversion of radians to degrees. We start by evaluating the arcsine function, which gives us the angle whose sine is 1. We then convert this angle from radians to degrees and add it to $-250^{\circ}$.

Q: What is the final answer to the expression $-250^{\circ} + 2 \arcsin (1)$?

A: The final answer to the expression is $110^{\circ}$.

Q: Can you explain the concept of radians and degrees?

A: Yes, certainly. Radians and degrees are two different units of measurement for angles. Radians are a more fundamental unit of measurement, and degrees are a derived unit. To convert radians to degrees, we use the formula: $1$ radian $= \frac{180}{\pi}$ degrees.

Q: How do you convert radians to degrees?

A: To convert radians to degrees, we use the formula: $1$ radian $= \frac{180}{\pi}$ degrees. We can also use a calculator or a computer program to perform the conversion.

Q: What is the range of the arcsine function?

A: The range of the arcsine function is typically restricted to the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$ to ensure that the function is one-to-one.

Q: Can you provide more information on the mathematical concepts used in the expression?

A: Yes, certainly. The expression $-250^{\circ} + 2 \arcsin (1)$ involves the use of the arcsine function, the conversion of radians to degrees, and the application of mathematical concepts such as addition and subtraction.

Conclusion

In this article, we answered some frequently asked questions related to the expression $-250^{\circ} + 2 \arcsin (1)$ and provided additional information to help readers understand the concept better. We hope that this article has been helpful in clarifying any doubts that readers may have had.

Frequently Asked Questions

• Q: What is the arcsine function? A: The arcsine function is the inverse of the sine function. It returns the angle whose sine is a given value.
• Q: How do you evaluate the expression $-250^{\circ} + 2 \arcsin (1)$? A: To evaluate the expression, we need to apply various mathematical concepts, including the use of the arcsine function and the conversion of radians to degrees.
• Q: What is the final answer to the expression $-250^{\circ} + 2 \arcsin (1)$? A: The final answer to the expression is $110^{\circ}$.

References

• [1] "Trigonometry" by Michael Corral, 2015.
• [2] "Calculus" by Michael Spivak, 2008.
• [3] "Mathematics for Computer Science" by Eric Lehman, 2018.

Further Reading

• For more information on the arcsine function, see [1].
• For more information on the conversion of radians to degrees, see [2].
• For more information on mathematical concepts, see [3].