Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles.
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Trigonometry
Standard: Trigonometry in Triangles - Understand how the trigonometric functions relate to right triangles, and solve word problems involving right and oblique triangles. Understand and apply the laws of sines and cosines. Use trigonometry to find the area of triangles.
Date Adopted or Revised: 09/07
Date of Last Rating: 06/07
Status: State Board Approved
Assessed: Yes


Example: In triangle ABC, tan A = 1/5. Find sin A and cot A. Example: Show that the slope of a line at 135º to the x-axis is the same as the tangent of 135º.


  • Reporting Category: Trigonometry
  • Item Type(s): This benchmark will be assessed using: MC , FR item(s)

  • Clarification :
    Students will solve real-world problems involving right-triangle trigonometry.
  • Content Limits :

    Items should not include special right triangles (30°-60°-90° and 45°-45°-90°) or the Pythagorean theorem.

    Angle measures will be in degree measure.

    Items will assess only sine, cosine, and tangent to determine the length of a side or an angle measure.

  • Stimulus Attributes :

    Items may be set in either real-world or mathematical contexts.

    Graphics should be used in all items.

  • Response Attributes :

    Fill-in response items may require the student to provide an angle measure or a length.

    Radian equivalents of correct answers will not be used as distractors.

    Fill-in response items will specify the nature of the response, if the response is not an integer.


  • Test Item #: Sample Item 1
  • Question:

    A tackle shop and restaurant are located on the shore of a lake and are 32 meters (m) apart. A boat on the lake heading toward the tackle shop is a distance of 77 meters from the tackle shop. This situation is shown in the diagram below, where point T represents the location of the tackle shop, point R represents the location of the restaurant, and point B represents the location of the boat.


    The driver of the boat wants to change direction to sail toward the restaurant. Which of the following is closest to the value of x?

  • Difficulty: N/A
  • Type: MC: Multiple Choice

  • Test Item #: Sample Item 2
  • Question:

    Mr. Rose is remodeling his house by adding a room to one side, as shown in the diagram below. In order to determine the length of the boards he needs for the roof of the room, he must calculate the distance from point A to point D.

  • Difficulty: N/A
  • Type: FR: Fill-in Response