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.
Time left: 00:00:00
Sample questions
- Solve sin x = ___ on [0°, 360°].
- Solve cos x = ___ on [0°, 360°].
- Solve tan x = ___ on [0°, 360°].
- Find the maximum value of y = a sin x + b cos x.
- What is the least positive period of y = cos x in degrees?
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.
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