A basic sine curve has a minimum value at intervals of
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minimum at
Grade 12 · MHF4U · Advanced Functions
MHF4U Trigonometric Functions Practice Test (with Solutions)
Trigonometric Functions takes the ratios and turns them into graphs. Your test will ask where the six trig functions have their zeros, maximums and asymptotes, for the mapping rule of a transformed sine, and for every solution to a trig equation between 0 and 2π. Try each question below before you open the answer.
Free Trigonometric Functions Practice Test
8 questions, exactly as a free account gets them in the first Trigonometric Functions test on Martian Lab. Try each one on paper first, then open the answer.
- The secant curve will have asymptotes at intervals of
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V.A. - The function(s) with zeros at intervals of are (full names not abbreviations or write the equations for the functions)
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- The solution(s) to , is/are
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- Rewrite as a single cosine function.
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- The solution(s) to , is/are
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- The mapping rule for is
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- A horizontal translation for trig. functions should be called a
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phase shift
This Unit on Martian Lab
The lessons go from graphing all six trig functions in radians to transformed sinusoidal functions, then finish with solving trig equations.
- Graphing Trigonometric Functions
- Sinusoidal Functions
- Trigonometric Equations
Then 4 full Trigonometric Functions practice tests to check yourself.
Start Trigonometric Functions freeTrigonometric Functions FAQ
What is on an MHF4U trigonometric functions test?+
Graphs of sine, cosine, tangent and their reciprocals in radians: period, zeros, maximums, minimums and asymptotes. Then transformations and mapping rules for sinusoidal functions, rewriting with compound angle formulas, and solving trig equations on 0 ≤ x ≤ 2π. The questions on this page cover each of these.
Where are the asymptotes of the reciprocal trig functions?+
Wherever the denominator is 0. Secant and tangent both divide by cos x, so they have asymptotes at x = π/2 + kπ. Cosecant and cotangent divide by sin x, so theirs are at x = kπ.
How do you write the mapping rule for a sinusoidal function?+
Write it as y = a sin[k(x - d)] + c, factoring k out of the bracket first. The mapping rule is (x, y) → (x/k + d, ay + c). For y = -4 sin[(2/3)(x + π/8)] + 7 that gives (3x/2 - π/8, -4y + 7).
How do you solve a trig equation between 0 and 2π?+
Find the reference angle from the special triangles, then use CAST to pick the quadrants where the ratio has the right sign. For cos x = -√3/2 the reference angle is π/6 and cosine is negative in quadrants 2 and 3, so x = 5π/6 or 7π/6. For sin 2x, solve for 2x on 0 to 4π first, then halve, which doubles the number of solutions.
What is a phase shift?+
The horizontal translation of a trig function, the d in y = a sin[k(x - d)] + c. Factor k out of the bracket before you read it off, or you will get the shift wrong.
Trigonometric Functions Topics
One idea at a time: a short explanation, then five worked examples.