LT

Test: Trigonometric functions and equations

This test covers graphs, periods, ranges and signs of sine, cosine and tangent functions. Tasks also develop solution of elementary trigonometric equations and selection of solutions within a stated interval.

Question qty: 10
Duration in minutes: 17
Start »

Time left: 00:00:00

Finish the test
List of tests
Start over

Sample questions

  • In which quadrants is sin x positive?
  • Find the maximum value of y = a sin x.
  • Solve tan x = s on [0°, 360°].
  • What is the least positive period of y = cos x in degrees?
  • How do algebraic and graphical solutions of a trigonometric equation differ?
  • Solve cos x = s on [0°, 360°].
  • What do solutions of f(x) = a represent on a graph?
  • Solve sin x = s on [0°, 360°].

Trigonometric functions and equations

Sine and cosine have period 2π, while tangent has period π. The identities sin²x + cos²x = 1 and tan x = sin x/cos x support transformations of trigonometric expressions.

General solutions

Solutions of sin x = a occur in two positions per period, while those of cos x = a are symmetric about the x-axis. Tangent solutions repeat every π. After writing a general solution, select the values in the required interval and confirm that the function is defined.

Related mathematics tests

Function properties and transformations

This test develops understanding of even and odd functions and common graph transformations. Students identify shifts, reflections and scaling and construct a new function formula from a given transformation.

Solve: Function properties and transformations

Higher-degree rational equations

This test focuses on cubic, biquadratic and other higher-degree equations. Students factor expressions, use substitution and verify which candidate values satisfy the original equation.

Solve: Higher-degree rational equations

Arithmetic and geometric progressions

This test develops recognition of arithmetic and geometric progressions and use of general-term formulas. Tasks include finding the common difference or ratio, determining missing terms and calculating sums of initial terms.

Solve: Arithmetic and geometric progressions

Irrational equations

This test develops methods for equations containing square and cube roots. Tasks require students to determine the domain, raise both sides to a power and check for extraneous solutions introduced during transformation.

Solve: Irrational equations