Trigonometric Functions Study Guide

1. Sine Function (sin)

   • The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
   • The sine function is periodic, with a period of 360 degrees (or 2π radians).
   • The range of the sine function is between -1 and 1.

2. Cosine Function (cos)

   • The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
   • Like the sine function, the cosine function is also periodic, with a period of 360 degrees (or 2π radians).
   • The range of the cosine function is also between -1 and 1.

3. Tangent Function (tan)

   • The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
   • Unlike the sine and cosine functions, the tangent function is not periodic.
   • The tangent function can take on any real value.

4. Cosecant, Secant, and Cotangent Functions

   • The cosecant (csc), secant (sec), and cotangent (cot) functions are the reciprocals of the sine, cosine, and tangent functions, respectively.
   • Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

5. Using Trigonometric Functions

   • Trigonometric functions are used to solve problems involving angles and sides of triangles.
   • They are also applied in various real-world situations, such as in physics, engineering, and navigation.