State two angles, one negative and one positive, co-terminal to .
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Grade 12 · MHF4U · Advanced Functions
MHF4U Trigonometric Ratios Practice Test (with Solutions)
Trigonometric Ratios is where trig moves to radians and starts leaning on identities. Expect to convert between degrees and radians, find coterminal and related angles, rewrite a ratio with a co-function identity and collapse an expression with a double angle formula. Do each question below on paper, then check the answer.
Free Trigonometric Ratios Practice Test
8 questions, exactly as a free account gets them in the first Trigonometric Ratios test on Martian Lab. Try each one on paper first, then open the answer.
- State an acute angle, in quadrant 1, that is co-related to .
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- Convert into radians as an exact value (keep as an improper fraction).
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- Convert into degrees.
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- A trig expression equal to , using a related, Q2, obtuse angle, is
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- A trig expression equal to , using a co-related Q1 acute angle, is
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- An equivalent co-related expression to is
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- Write as a single trig ratio.
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This Unit on Martian Lab
The lessons start with trigonometry in radians, then cover co-function identities, the compound and double angle formulas, and trig identities.
- Trigonometry
- Co-function Identities
- Double Compound Angle Formula
- Trigonometric Identities
Then 4 full Trigonometric Ratios practice tests to check yourself.
Start Trigonometric Ratios freeTrigonometric Ratios FAQ
What is on an MHF4U trigonometric ratios test?+
Radian measure, coterminal and related angles, exact values from the unit circle, co-function identities, the compound and double angle formulas, and proving trig identities. The free questions on this page cover radians, coterminal and related angles, co-function identities and the double angle formula.
How do you convert between degrees and radians?+
Multiply degrees by π/180 to get radians, and multiply radians by 180/π to get degrees. So 680° is 680π/180 = 34π/9, and 7π/15 is 7(180)/15 = 84°.
What is a coterminal angle?+
An angle with the same terminal arm. Add or subtract 2π (or 360°) as many times as you like: 4π/5 + 2π = 14π/5 and 4π/5 - 2π = -6π/5 are both coterminal with 4π/5.
How do co-function identities work?+
Shifting by π/2 or 3π/2 swaps a ratio for its co-ratio: sine and cosine, tangent and cotangent, secant and cosecant. For example cos(π/2 - x) = sin x. Use CAST on the original angle to get the sign, so cot(3π/2 + x) becomes -tan x.
When do you use the double angle formula?+
Whenever you see sin x cos x of the same angle, or need sin 2x or cos 2x in terms of x. Since sin 2x = 2 sin x cos x, an expression like 3 sin(x/2) cos(x/2) is (3/2) sin x.
Trigonometric Ratios Topics
One idea at a time: a short explanation, then five worked examples.