Chapter 14 Trigonometric Identities and Equations

Get Ready!

• Lesson 4-5 Solving Quadratic Equations

  Solve each equation.

  1. 4 x 2 = 25 4 x squared , equals 25
  2. x 2 − 23 = 0 x squared , minus 23 equals 0
  3. 3 x 2 = 80 3 x squared , equals 80
  4. 8 x 2 − 44 = 0 8 x squared , minus 44 equals 0
  5. 0.5 x 2 = 15 0.5 , x squared , equals 15
  6. 6 x 2 − 13 = 11 6 x squared , minus 13 equals 11

• Lesson 6-7 Finding the Inverse of a Function

  For each function f, find f − 1 f super negative 1 end super and the domain and range of f and f − 1 . f super negative 1 end super , . Determine whether f − 1 f super negative 1 end super is a function.

  7. f ( x ) = 5 x + 2 f open x close equals 5 x plus 2
  8. f ( x ) = x + 3 f , open x close , equals , square root of x plus 3 end root
  9. f ( x ) = 3 x − 4 f , open x close , equals . square root of 3 x minus 4 end root
  10. f ( x ) = 5 x f open x close equals , 5 over x
  11. f ( x ) = 10 x − 1 f , open x close , equals . fraction 10 , over x minus 1 end fraction
  12. f ( x ) = 10 x − 1 f open x close equals , 10 over x , minus 1

• Lesson 7-5 Solving Exponential and Logarithmic Equations

  Solve each equation.

  13. 4 x = 1 8 4 x equals , 1 eighth
  14. log 5 x + 1 = − 1 log 5 x plus 1 equals negative 1
  15. 7 3 x = 500 7 , 3 to the x , equals 500
  16. log 3 x + log x = 9 log 3 x plus log x equals 9
  17. log ( 4 x + 3 ) − log x = 5 log open 4 x plus 3 close minus log x equals 5
  18. 3 x = 243 3 to the x , equals 243

• Lessons 13-4, 13-5, and 13-6 Evaluating Trigonometric Functions

  For each value of θ , theta comma find the values of cos θ , sin θ , cosine theta comma . sine theta comma and tan θ . tangent theta . Round your answers to the nearest hundredth.

  19. 48 ° 48 degrees
  20. − 105 ° negative 105 degrees
  21. 16 ° 16 degrees
  22. 5 π 6 fraction 5 pi , over 6 end fraction

Table of Contents