## Write The Expression As The Sine, Cosine, Or Tangent Of An Angle. Sin 57° Cos 13° – Cos 57° Sin 13°

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## Answer ( 1 )

## Write The Expression As The Sine, Cosine, Or Tangent Of An Angle. Sin 57° Cos 13° – Cos 57° Sin 13°

## Introduction

The trigonometric functions of Sine, Cosine, and Tangent are essential tools for understanding how angles measure along the circumference of a circle. But what happens when you’re asked to write an expression using these functions? In this blog post, we’ll look at one such example: Write the expression as the sine, cosine, or tangent of an angle. The expression in question is “sin 57° cos 13° – cos 57° sin 13°”. We’ll walk through how to solve this problem step-by-step and investigate what each part of the equation means. By the end, you’ll have a better understanding of how to use sine, cosine, and tangent to work with expressions.

## The Sine, Cosine, and Tangent of an Angle

In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in many areas, such as engineering, navigation, design, and physics.

The three most common trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These are usually denoted by the letters S, C, and T. The inverse trigonometric functions are usually denoted by Arcsin(sin-1), Arccos(cos-1), and Arctan(tan-1).

To find the value of these trigonometric functions for a given angle, we use a right-angled triangle. The angle is usually denoted by θ (theta).

## The Sin of 57°

The Sin of 57°

We all know that the sin of an angle is the ratio of the opposite side to the hypotenuse. But what if we don’t know the sides? How do we find the sin of 57°?

First, let’s draw a picture. We’ll put the angle at 57° in the middle and label the sides:

Now we can see that, to find the sin of 57°, we just need to find the ratio of Side A to Side B. We can do this using a little trigonometry.

First, we’ll use the cosine function. The cosine of an angle is the ratio of the adjacent side to the hypotenuse. In our case, that’s Side B over Side C. So we can write:

cos(57°) = Side B / Side C

Now we can solve for Side B:

Side B = cos(57°) * Side C ~~ 0.74 * Side C

## The Cosine of 13°

To find the cosine of 13°, we can use the fact that cos(x) = sin(90-x). Therefore, cos(13) = sin(77).

## The Tangent of 57°

The tangent of 57° is the ratio of the side opposite 57° to the side adjacent to 57°. Tangent is abbreviated as tan. Therefore, we can write:

tan 57° = opposite/adjacent

To find the value of the tangent, we need to know the lengths of the sides. We can use a scientific or graphing calculator to find these values. With a calculator, we would input 57° into the “tan” function and hit the equals sign; this would give us the value of 1.732 (to three decimal places).

## Conclusion

The expression Sin 57° Cos 13° – Cos 57° Sin 13° can be written as the sine, cosine and tangent of an angle. When simplified, this expression equals -sin(70°). This equation is a useful way to remember the relationship between sines and cosines when working with angles. With these simple steps, you will quickly be able to calculate any angle from its corresponding sin or cos values.