Trigonometric Functions

Topics in this chapter

• Trigonometric Ratios and Standard Values
• Quadrants, Signs, and Periodicity
• Trigonometric Functions, Domain and Range
• Identities and Expression Simplification
• Compound and Multiple-Angle Formulas
• Trigonometric Equations and Solutions

Cheat sheet

Practice questions

1. Question 1Q-063620

   The value of sin(7π/6) is:

   1. A.1/2
   2. B.-1/2
   3. C.√3/2
   4. D.-√3/2
   See the answer and solution
2. Question 2Q-FCDDD4

   What is the fundamental period of the function f(x) = sin(3x) + cos(3x)?

   1. A.π/3
   2. B.2π/3
   3. C.π
   4. D.2π
   See the answer and solution
3. Question 3Q-10AF1C

   How many solutions does the equation 2sin²x − 3sin x + 1 = 0 have in the interval [0, 2π]?

   1. A.1
   2. B.2
   3. C.3
   4. D.4
   See the answer and solution
4. Question 4Q-437BEA

   For all real values of x for which the expressions are defined, prove that (1 − cos x)/sin x = sin x/(1 + cos x).

   See the answer and solution
5. Question 5Q-9DE53D

   If $\tan \theta=-\frac{5}{12}$ and $\theta$ lies in the fourth quadrant, then $\sin \theta$ is:

   1. A.$\frac{5}{13}$
   2. B.$-\frac{5}{13}$
   3. C.$\frac{12}{13}$
   4. D.$-\frac{12}{13}$
   See the answer and solution