Chapter 14 - Algebra Coach Exercises


Algebra Coach Exercise on right triangle trigonometry.
Each of the following questions gives some information about the right triangle shown to the right. Drag-and-drop this information into the Algebra Coach’s list box. Then drag one of the “list of equations to use” into the listbox (whichever one allows you to find the required side or angle) and click OK. Then click on Substitute to substitute the values into the equation. Then click on AutoSolve to solve the equation for the required value.

Required Options settings: Set degrees/radians mode to “degrees”. Set exact/floating point mode to “floating point”. Set the AutoSolve unknown to the required angle or side.


In questions 1 to 4 use the information provided to find angle A.
  1. a = 226, b = 313
  2. a = 192, c = 212
  3. b = 12, c = 41
  4. a = 5, b = 12
Find the missing side: a, b or c.
  1. a = 226, b = 313
  2. a = 192, c = 212
  3. b = 12, c = 41
  4. a = 5, b = 12
Find the two missing sides. Angle A is given in degrees.
  1. A = 40, b = 313
  2. A = 74, c = 212
  3. A = 22, a = 41
  4. A = 5, b = 12
List of equations to use:   
  • sin(A) = a / c
  • cos(A) = b / c
  • tan(A) = a / b

  • c^2 = a^2 + b^2
  • A + B + 90 = 180


Algebra Coach Exercise on oblique triangle trigonometry.
Each of the following questions gives some information about the oblique triangle shown to the right. Drag-and-drop this information into the Algebra Coach’s list box. Then drag one of the “list of equations to use” into the listbox (whichever one allows you to find the required side or angle) and click OK. Then click on Substitute to substitute the values into the equation. Then click on AutoSolve to solve the equation for the required value.

Required Options settings: Set degrees/radians mode to “degrees”. Set exact/floating point mode to “floating point”. Set the AutoSolve unknown to the required angle or side.


In questions 1 and 2 use the information provided to find the three angles: A, B and C.
  1. a = 22, b = 31, c = 28
  2. a = 19, b= 14, c = 30
Find the missing sides and angles. (All angles are given in degrees. Note that #6 is an example of the ambiguous case.)
  1. a = 226, A = 32.5, B = 49.7
  2. a = 192, b = 122, C = 22.2
  3. a = 47, b = 32, A = 25
  4. a = 14, b = 32, A = 25
List of equations to use:                           
  • sin(A) / a = sin(B) / b
  • sin(B) / b = sin(C) / c
  • sin(C) / c = sin(A) / a

  • a^2 = b^2 + c^2 - 2 b c cos(A)
  • b^2 = a^2 + c^2 - 2 a c cos(B)
  • c^2 = a^2 + b^2 - 2 a b cos(C)

  • A + B + C = 180


Algebra Coach Exercise on graphs of trigonometric functions.
Graph each of the following functions. To do this drag-and-drop each of them into the Algebra Coach and click the Graph button. Required Options settings: Set degrees/radians mode to “radians” and set the letter p to represent the number π.

These are the three basic trigonometric functions.
  1. y = sin(x)
  2. y = cos(x)
  3. y = tan(x)
These are their reciprocals, also known as the cotangent, secant and cosecant functions, respectively.
  1. y = 1 / tan(x)
  2. y = 1 / cos(x)
  3. y = 1 / sin(x)
These three waveforms differ only in their amplitude.
  1. y = sin(x), y = 3 sin(x), y = 5 sin(x)
These three waveforms differ only in their angular velocity.
  1. y = 5 sin(x), y = 5 sin(1.1 x), y = 5 sin(1.2 x)
These three waveforms differ only in their phase angle.
  1. y = 4 sin(x), y = 4 sin(x + p/4), y = 4 sin(x + p/2)

Algebra Coach Exercise on trigonometric identities.
Simplify each of the following trigonometric expressions. To do this drag-and-drop each of them into the Algebra Coach and click the Simplify button.
  1. sin(-x) + cos(-x) + tan(-x)
  2. sin(a + p/2) + cos(a + p) + tan(a + 2p)
  3. sin(a)/cos(b) + sin(c)/cos(c)
  4. tan(b+p/2)
  5. cos(y)^2 + sin(x)^2 + sin(y)^2
  6. sin(arctan(x)) - sin(arccos(sqrt(3)/2))

Algebra Coach Exercise on trigonometric equations.
Solve each of the following trigonometric equations. To do this drag-and-drop each of them into the Algebra Coach and click the AutoSolve button.
  1. a sin(x) + b = c
  2. a sin(5x) = b sin(10x)
  3. 3 sin(x) = 2 cos(2x) + 1
  4. 3 sin(8x) + 4 cos(8x) = 0
  5. 3 sin(6x) - 2 cos(6x) = 0