## Introduction

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has numerous applications in fields such as physics, engineering, and navigation. However, the subject can be challenging for many students. This article aims to provide a basic review of trigonometry concepts and offer an answer key for common problems.

### Trigonometric Functions

Trigonometric functions are the basic building blocks of trigonometry. There are six functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function is defined in terms of the ratios of the sides of a right triangle. For example, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

### Angles

Angles are central to trigonometry. An angle is a measure of the amount of rotation between two rays that share a common endpoint, called a vertex. Angles can be measured in degrees or radians. One complete rotation is 360 degrees or 2π radians.

### Pythagorean Theorem

The Pythagorean theorem is a fundamental theorem in trigonometry. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem is used extensively in trigonometry to calculate the lengths of sides of right triangles.

### Trigonometric Identities

Trigonometric identities are equations that are true for all values of the variables. There are many trigonometric identities, but some of the most important ones include the Pythagorean identity, the reciprocal identities, and the quotient identities.

### Inverse Trigonometric Functions

Inverse trigonometric functions are used to find the angle that corresponds to a given trigonometric ratio. For example, the inverse sine function returns the angle whose sine is a given value. Inverse trigonometric functions are important in applications such as navigation and engineering.

### Law of Sines

The law of sines is used to find the lengths of sides and the measures of angles in non-right triangles. It states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides of a triangle.

### Law of Cosines

The law of cosines is also used to find the lengths of sides and the measures of angles in non-right triangles. It states that the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the angle between them.

### Applications

Trigonometry has numerous applications in real-life situations. For example, it is used in navigation to calculate the distance between two points on the earth's surface. It is also used in engineering to design structures such as bridges and buildings.

### Conclusion

Trigonometry is a challenging subject, but with practice and a good understanding of the basic concepts, anyone can become proficient in it. This article has provided a review of some of the most important concepts and an answer key for common problems. With this knowledge, readers can tackle more advanced trigonometry topics and apply them to real-world situations.