What is the fundamental period of the function f(x) = 3tan(2x - pi/4) + 1?
Answer and explanation
Correct answer: A. pi/2
- Step 1: The fundamental period of the standard tangent function tan(u) is pi.
- Step 2: For tan(k*x), the period is pi / |k|.
- Step 3: Here k = 2, so the period is pi / 2.
Answer
pi/2.
Why not the others: pi is the period of standard tan(x); 2*pi is the period of sine and cosine; pi/4 confuses the phase shift with the period.
Practise more Differential and Integral Calculus and Complex Numbers.
Free questions with an explanation for every one, and full timed Bagrut (Secondary School Matriculation) mock tests.
More Differential and Integral Calculus and Complex Numbers questions
- Solve the trigonometric equation 2sin(x)^2 - 3sin(x) + 1 = 0 on the interval [0, 2*pi].
- Which expression is identical to cos(2*x) / (cos(x) + sin(x)) where defined?
- Find all real solutions to sin(3*x) + sin(x) = cos(x) on the interval [0, pi].
- If sin(x) = 3/5 and x is in the second quadrant (pi/2 < x < pi), what is the exact value of tan(2*x)?
- Determine all intersection points of y = 2cos(x) and y = 1/cos(x) on the interval [0, 2pi].
- Evaluate the trigonometric limit: lim_{x -> 0} (1 - cos(4x)) / (x sin(2*x)).