If \[$-6\$\] Is In \[$\cdot\$\] And $\theta=45^{\circ}$, Find The Value Of $c$. Round Your Answer To The Nearest Hundredth.

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Introduction

In trigonometry, the concept of a unit circle is crucial for understanding various trigonometric functions. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is used to define the trigonometric functions sine, cosine, and tangent. In this article, we will explore how to find the value of cc when ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}.

Understanding the Problem

To solve this problem, we need to understand the concept of a unit circle and how it relates to the given information. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. The angle θ\theta is measured in radians or degrees, and it is used to define the trigonometric functions sine, cosine, and tangent.

The Unit Circle

The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is used to define the trigonometric functions sine, cosine, and tangent. The unit circle is divided into four quadrants, each with a different sign for the x and y coordinates.

Finding the Value of cc

To find the value of cc, we need to use the given information and the concept of the unit circle. We are given that ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}. This means that we need to find the value of cc when the angle θ\theta is 45∘45^{\circ}.

Using the Unit Circle

To find the value of cc, we can use the unit circle and the given information. We know that the angle θ\theta is 45∘45^{\circ}, and we need to find the value of cc when ${-6}$ is in ${\cdot}$. We can use the unit circle to find the value of cc.

Finding the Value of cc Using the Unit Circle

To find the value of cc, we can use the unit circle and the given information. We know that the angle θ\theta is 45∘45^{\circ}, and we need to find the value of cc when ${-6}$ is in ${\cdot}$. We can use the unit circle to find the value of cc.

Calculating the Value of cc

To calculate the value of cc, we can use the following formula:

c = \frac{${-6}$}{${\sin(\theta)}$}

We know that θ=45∘\theta=45^{\circ}, so we can substitute this value into the formula:

c = \frac{${-6}$}{${\sin(45^{\circ})}$}

Evaluating the Sine Function

To evaluate the sine function, we can use the fact that sin⁡(45∘)=22\sin(45^{\circ})=\frac{\sqrt{2}}{2}. We can substitute this value into the formula:

c = \frac{${-6}$}{${\frac{\sqrt{2}}{2}}$}

Simplifying the Expression

To simplify the expression, we can multiply the numerator and denominator by 2\sqrt{2}:

c = \frac{${-6\sqrt{2}}$}{${2}$}

Evaluating the Expression

To evaluate the expression, we can divide the numerator by the denominator:

c = ${-3\sqrt{2}}$

Rounding the Answer

To round the answer to the nearest hundredth, we can use a calculator to evaluate the expression:

c \approx ${-4.24}$

Conclusion

In this article, we explored how to find the value of cc when ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}. We used the unit circle and the given information to find the value of cc. We calculated the value of cc using the formula c = \frac{{-6}}{{\sin(\theta)}} and evaluated the expression to find the value of cc. We rounded the answer to the nearest hundredth to find the final value of cc.

Final Answer

The final answer is \boxed{{-4.24}}.

Introduction

In our previous article, we explored how to find the value of cc when ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}. We used the unit circle and the given information to find the value of cc. In this article, we will answer some common questions related to this topic.

Q&A

Q: What is the unit circle and how is it used in trigonometry?

A: The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is used to define the trigonometric functions sine, cosine, and tangent. The unit circle is divided into four quadrants, each with a different sign for the x and y coordinates.

Q: How do I find the value of cc when ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}?

A: To find the value of cc, you can use the formula c = \frac{{-6}}{{\sin(\theta)}}. You can substitute the value of θ\theta into the formula and evaluate the expression to find the value of cc.

Q: What is the value of sin⁡(45∘)\sin(45^{\circ})?

A: The value of sin⁡(45∘)\sin(45^{\circ}) is 22\frac{\sqrt{2}}{2}.

Q: How do I simplify the expression c = \frac{{-6\sqrt{2}}}{{2}}?

A: To simplify the expression, you can multiply the numerator and denominator by 2\sqrt{2}.

Q: What is the final value of cc when rounded to the nearest hundredth?

A: The final value of cc is ${-4.24}$.

Q: Can I use a calculator to find the value of cc?

A: Yes, you can use a calculator to find the value of cc. Simply enter the values of ${-6}$ and sin⁡(45∘)\sin(45^{\circ}) into the calculator and evaluate the expression.

Q: What is the significance of the unit circle in trigonometry?

A: The unit circle is a fundamental concept in trigonometry and is used to define the trigonometric functions sine, cosine, and tangent. It is a powerful tool for solving problems involving right triangles and is used extensively in mathematics and physics.

Conclusion

In this article, we answered some common questions related to finding the value of cc when ${-6}$ is in ${\cdot}$ and θ=45∘\theta=45^{\circ}. We provided explanations and examples to help clarify the concepts and procedures involved. We hope that this article has been helpful in understanding the unit circle and how it is used in trigonometry.

Final Answer

The final answer is \boxed{{-4.24}}.