2.8 Trigonometric ratios of angles in radians

Triangles, angles, sides and hypotenuse, - these are the basic parts of Trigonometry. In this chapter we will brush up on these parts once more. By now you are already familiar with the radian. The radian is the term used to define the measure of a standard angle. It is defined that the measure of the radian is equal to that of the length of its corresponding arc.

In this chapter we will learn about the different types of angles such as the standard angles, reference angles and co-terminal angles. Standard angles, if you would recall from our previous chapter, are angles that are formed by the intersection of a ray and the x axis. The x axis is referred to as the initial side and the ray is referred to as the terminal side. Take note that standard angles have their vertices in the center of a unit circle. We also discussed in that same chapter about the reference angles, which are the angles associated with the angles in every standard angle. The reference angles are the acute angle formed by the terminal side of the standard angle and the x axis. The last kind of angle is the co-terminal angles, which as the word suggests are angles that have the same terminal sides. We will get to learn more about these angles from chapter 8.1 to 8.3.

In the next two parts of the chapter, we will learn about the general form of the different trigonometric functions. This will help us find the exact values of the trigonometric functions as well as use the ASTC rule in Trigonometry.

In 8.6 to 8.8 we will review what we have learned before about a unit circle, and the such as the definition of the radians, and the length of the arc, converting between the measures of the angles, and the trigonometric ratios of angles in radians.

Trigonometric ratios of angles in radians

Lessons

  • 1.
    Find the value
  • 2.
    Determine one positive angle and one negative angle that is coterminal with:
    • a)
      sin 123°
    • b)
      sin 123 123
    • c)
      cos 200 -200
    • d)
      tan 13π7 {{13 \pi} \over 7 }
    • e)
      sin π\pi
    • f)
      sin π\pi °
    • g)
      sec 500 °
Teacher pug

Trigonometric ratios of angles in radians

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