Question

1. # If Sine Of X Equals 1 Over 2, What Is Cos(X) And Tan(X)? Explain Your Steps In Complete Sentences.

The Trigonometric Functions of Sine, Cosine, and Tangent (also known as Sin, Cos, and Tan) are essential tools for any math student’s toolbox. In this article, we will explore a step-by-step process of solving a trigonometry problem involving the Sine function. We will be specifically looking at the equation “sin(x) = 1/2” and determining what the values of cos(x) and tan(x) would be. By working through this example, you can get a better understanding of how to use trigonometric functions in your own work.

## The Sine of X

The sine of x is defined as the ratio of the side opposite to the angle x in a right angled triangle to the hypotenuse of the triangle. Sine of x is represented by sin(x).
If we take a look at the unit circle, we can see that the sine of x is equal to the y-coordinate of the point on the unit circle where x intersects it. This means that if we were to draw a line from (0,0) to (x,y), where y is equal to sin(x), then the angle between this line and the positive x-axis would be equal to x.

We can also see from the unit circle that cos(x) is equal to the x-coordinate of the point on the unit circle where x intersects it. This means that if we draw a line from (0,0) to (x,y), where y is equal to cos(x), then the angle between this line and the positive x-axis would be equal to x.

Similarly, we can see that tan(x) is equal to sin(x)/cos(x). This means that if we draw a line from (0,0) to (x,y), where y is equal to tan(x), then the angle between this line and the positive x-axis would be equal to x.

## Cos(X) and Tan(X)

The cosine of x is equal to the sine of x divided by the cosine of x. The tangent of x is equal to the sine of x divided by the cosine of x.

## How to find Cos(X) and Tan(X)

To find cos(x), we can use the Pythagorean theorem. First, we draw a right triangle. Then, we label the sides of the triangle. The hypotenuse is the side opposite the 90 degree angle, and is always labeled “c.” The side adjacent to angle x is labeled “a,” and the remaining side is labeled “b.” Now, we can use the Pythagorean theorem to solve for “a.” We know that a^2 + b^2 = c^2, so we can rearrange this equation to get a = sqrt(c^2 – b^2). Now that we know the value of “a,” we can use it to find cos(x). Cos(x) = a/c. To find tan(x), we use a similar method. First, we draw a right triangle and label the sides. Then, we use the Pythagorean theorem to solve for “b.” We know that b^2 = c^2 – a^2, so b = sqrt(c^2 – a^2). Now that we know the value of “b,” we can use it to find tan(x). Tan(x) = b/a.

## Conclusion

In conclusion, when given a sine value of 1/2, one can calculate the cosine and tangent value by using the Pythagorean identity along with some basic trigonometric functions. By beginning with the definition of sine as “opposite side over hypotenuse”, we can then use the reciprocal identities to solve for cos and tan in terms of sin. This method provides an efficient way to attain both values quickly and easily.

2. In mathematics, trigonometry is the study of relationships between the sides and angles of triangles. Specifically, the sine, cosine, and tangent functions are used to relate a given angle in a triangle to its sides. If we know one side or angle of a triangle, it’s possible to calculate the other two using these three functions.

For example, if we know that sin(x) = 1/2 then by using basic trigonometric identities we can find out that cos(x) =√3/2 and tan(x) = √3/3. To find this solution, we first use Pythagoras’ theorem to calculate the length of one side: x^2 + (1/2)^2 = 1.

3. Are you ready to explore the world of trigonometry and find out what happens when the sine of an angle is equal to one-half? Let’s dive in!

When the sine of an angle x is equal to one-half, the cosine and tangent of x can be calculated. In order to find out cos(x) and tan(x), we first need to understand the relationship between sine and cosine.

The sine and cosine of an angle x are related by the equation:

sin(x) = cos(90° – x)

This means that if we know the sine of an angle, we can use this equation to calculate the cosine of the angle.

In this case, the sine of x is equal to one-half, so the cosine of x can be calculated by plugging this value into the equation above:

cos(x) = sin(90° – x)

cos(x) = sin(90° – (1/2))

cos(x) = sin(89.5°)

Using a scientific calculator, we can calculate the sine of 89.5° which gives us a result of 0.987688. Therefore, if the sine of an angle x is equal to one-half, the cosine of x is equal to 0.987688.

Now that we know the cosine of x, we can calculate the tangent of x. The tangent of an angle x is related to the sine and cosine of x by the equation:

tan(x) = sin(x) / cos(x)

Using the values we just calculated, we can plug these into the equation above:

tan(x) = (1/2) / 0.987688

tan(x) = 0.506446

Therefore, if the sine of an angle x is equal to one-half, the cosine of x is equal to 0.987688 and the tangent of x is equal to 0.506446.

We hope this explanation was helpful and that you now understand how to calculate the cosine and tangent of an angle given the sine of the angle.

4. ‍ Have you ever been confused by a trigonometry question involving sine, cosine and tangent? If so, you’ve come to the right place!

In this blog post, we’ll answer the question, “If sine of x equals 1/2, what is cos(x) and tan(x)?” and explain our steps in complete sentences.

First, let’s begin by reviewing the definitions of sine, cosine and tangent. Sine is the ratio of the opposite side to the hypotenuse of a right triangle. Cosine is the ratio of the adjacent side to the hypotenuse of a right triangle. Tangent is the ratio of the opposite side to the adjacent side of a right triangle.

Now we can answer our original question. If the sine of x is 1/2, we can use the Pythagorean theorem to find the hypotenuse of the right triangle. The hypotenuse is equal to the square root of 2. Therefore, since the sine of x is 1/2, the opposite side is equal to 1.

Since we now know the opposite side and the hypotenuse, we can calculate the cosine of x: cos(x) = adjacent side/hypotenuse. Therefore, cos(x) = 1/√2.

We can also calculate the tangent of x: tan(x) = opposite side/adjacent side. Therefore, tan(x) = 1/1 = 1.

Therefore, if the sine of x equals 1/2, then the cosine of x equals 1/√2 and the tangent of x equals 1.

We hope this blog post has helped you understand the answer to the question, “If sine of x equals 1/2, what is cos(x) and tan(x)?”