Grade 11 Trigonometric Functions Worksheets
Free printable trigonometric functions practice for Grade 11 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 11 Trigonometric Functions Practice
Solve each problem. Show your work.
- 1.Convert 60° to radians: _____
- 2.Give the exact value of sin 150°: _____
- 3.Use the CAST rule to state the signs of sine and cosine at 210°: _____
- 4.Convert 120° to radians: _____
- 5.Give the exact value of sin 225°: _____
- 6.Use the CAST rule to state the signs of sine and cosine at 240°: _____
Show answer key
- Question 1: π/3
- Question 2: 1/2
- Question 3: sine negative; cosine negative
- Question 4: 2π/3
- Question 5: -√2/2
- Question 6: sine negative; cosine negative
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Convert the angle 3 * pi / 4 radians into degrees.
- 2.Find the exact value of sin(pi / 6) using the unit circle.
- 3.Determine the amplitude of the function y = 3 * sin(x).
- 4.State the period of the function y = cos(2x).
- 5.If tan(theta) = 1 and theta is in Quadrant III, what is the value of sin(theta)?
- 6.Simplify the expression sin²(x) + cos²(x) - 1.
Full range of grade expectations
Solve each problem. Show your work.
- 1.Convert the angle 5pi/6 radians to degrees and determine the exact coordinates (x, y) on the unit circle for this angle.
- 2.Given sin(theta) = 3/5 and theta is in the second quadrant, find the exact values of cos(theta) and tan(theta).
- 3.Determine the amplitude, period, and phase shift for the function f(x) = 3*sin(2x - pi/2) + 1.
- 4.Prove the identity: (sin(x) / cos(x)) + (cos(x) / sin(x)) = 1 / (sin(x)cos(x)).
- 5.A Ferris wheel with a radius of 10 meters rotates once every 60 seconds. The center of the wheel is 12 meters above the ground. If a rider starts at the bottom of the wheel at t = 0, write a sinusoidal function h(t) that represents the rider's height above the ground at time t.
- 6.The depth of water in a harbor varies sinusoidally with the tides. The high tide is 10 meters and the low tide is 2 meters. The time between a high tide and the next low tide is 6 hours. If a high tide occurs at t = 0, find the depth of the water at t = 4 hours.
What Your Child Will Learn
This unit extends trigonometry beyond right triangles into the full circular functions, starting with angles in standard position and the CAST rule for determining the sign of trig ratios in each quadrant. Students learn radian measure as an alternative to degrees, converting fluently between the two, and use the unit circle to determine exact trigonometric values for common angles without a calculator.
Graphing becomes central: students sketch y = sin(x), y = cos(x), and y = tan(x), then analyze how changes to amplitude, period, phase shift, and vertical shift transform these graphs — skills that mirror the transformation thinking used with quadratics and exponentials earlier in the course. Trigonometric identities, including the reciprocal, quotient, and Pythagorean identities, are introduced and used to simplify expressions and verify equivalences.
Applications include modelling periodic phenomena such as tides, sound waves, and Ferris wheel motion, where students must translate a real-world cyclical pattern into a sine or cosine equation and use it to answer questions about timing and height. This periodic-modelling skill is a distinctive and practical payoff of the entire trigonometry strand.
Skills Covered
- Determining trig ratios using the CAST rule and reference angles
- Converting between degree and radian measure
- Using the unit circle to find exact trigonometric values
- Graphing and transforming sine, cosine, and tangent functions
- Applying reciprocal, quotient, and Pythagorean identities
- Modelling periodic real-world phenomena with trig functions
Curriculum Aligned: Strand of Grade 11 Functions (MCR3U) covering trigonometric functions, radian measure, and periodic modelling — distinct from the right-triangle focus in Grade 10.
Parent Tip: You likely won't recall radian conversions from your own schooling, and that's fine — a useful move is to have your teen sketch the graph of their answer and describe what it represents (a wave repeating every so many hours, say). If the shape and story match the word problem, the model is probably right.
What your child will practice
- Graphing Sine and CosineGraph and analyse sine and cosine functions, identifying amplitude, period, and phase shift.
- Trigonometric IdentitiesProve simple trigonometric identities using fundamental identities.
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Check my workFrequently Asked Questions
How often should my child practice trigonometric functions?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.