Duration of the online course: 4 hours and 29 minutes
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Boost your Grade 11 trig skills fast with this free online course—master CAST, reductions, identities and equations with exam-style practice.
In this free course, learn about
Use CAST to determine trig ratio signs in quadrants and find cos/sin/tan from a given ratio
Build/interpret right triangles on the Cartesian plane to compute sin, cos, tan using Pythagoras
Apply complementary and allied-angle identities (e.g., sin(90-x), sin(180+x), sin(360-x))
Reduce angles beyond 360° and simplify expressions like tan(720-x) using periodicity and CAST
Evaluate trig sums/products with special angles and exact values (e.g., cos178+cos179+cos180)
Use core identities: sin²x+cos²x=1, tanx=sinx/cosx, cotx=cosx/sinx, 1+tan²x=sec²x
Algebraic simplification of complex trig expressions into single ratios or constants
Solve basic trig equations in degrees on [0,360) and write general solutions with k∈Z
Solve trig equations by substitution (quadratic in sin/cos) and check valid solutions
Find reference angles via inverse trig and use them to locate solutions in correct quadrants
Work with trig graphs/domain ideas (where functions are defined) and interpret restrictions
Geometry/ratio problems on line segments using similar triangles and coordinate scaling
About the free online course
Trigonometry becomes much easier once you know how to read angles with confidence, choose the correct sign in each quadrant, and simplify expressions without guessing. This free online Grade 11 trigonometry course builds those habits step by step, helping you move from basic ratios to the kind of algebraic and exam reasoning that earns marks consistently.
You will practise using the CAST diagram to identify whether sine, cosine, or tangent should be positive or negative in each quadrant, and apply that thinking to triangles drawn on the Cartesian plane. By working with given ratios such as sin(θ) and finding other ratios like cos(θ) in the correct quadrant, you strengthen your ability to connect geometry, coordinates, and trigonometric relationships instead of memorizing isolated rules.
As you progress, you will learn to reduce angles confidently, including turns beyond 360° and special cases like 90°, 180°, 270°, and 720°, so that complex-looking expressions become familiar and manageable. Complementary-angle relationships, reference angles, and quadrant reasoning are emphasized to make simplification feel logical rather than procedural.
The course also develops fluency with core identities used throughout Grade 11, including relationships that convert between functions and expressions that collapse to 1 or a single ratio. You will gain practice simplifying multi-step expressions involving sin, cos, tan, cot, and squared terms, which is essential for tests where method and accuracy matter as much as the final answer.
Finally, you will apply these tools to solving trigonometric equations and interpreting solutions on the interval, including finding general solutions, checking validity, and working with inverse trigonometric ideas and reference angles. With exam-style questions that mirror classroom assessments, you will leave better prepared to simplify confidently, solve faster, and avoid common sign and quadrant errors.
Course content
Video class: Trigonometry grade 11: Triangle on CAST23m
Exercise: Given that \( \sin(\theta) = \frac{3}{5} \), \( \theta \) is in the second quadrant, and you need to find \( \cos(\theta) \). What is \( \cos(\theta) \)?
Video class: Trigonometry grade 11: Triangle on CAST Practice02m
Exercise: Given a right triangle where one of the angles is 37 degrees and the sine of this angle is k, which of the following expressions represents cos(53 degrees) in terms of k?
Video class: Trigonometry grade 11: Triangle on CAST Practice02m
Exercise: Given a right triangle in which one vertex lies at the origin and another at (-5, -12), what is the value of sin α, where α is the angle opposite the vertical leg of the triangle?
Video class: Reduction grade 1121m
Exercise: Using the CAST diagram, which of the following is the correct reduction for sin(270 - x)?
Video class: Reduction grade 11: Using Numbers and special angles.16m
Exercise: Given the trigonometric expression tan(720 - x), which quadrant does the angle correspond to on the CAST diagram and how can it be simplified?
Video class: Reduction grade 11: practice17m
Exercise: If \( \sin(90^\circ - x) \) equals \( \cos(x) \), which trigonometric identity does this statement represent based on complementary angles?
Video class: Reduction Grade 11: Exam04m
Exercise: Evaluate the following expression using trigonometric identities: cos(178°) + cos(179°) + cos(180°).
Video class: Reduction grade 11: practice03m
Exercise: Simplify the expression sin(360 - x) - 1 to a single trigonometric term.
Video class: Reduction grade 11: practice01m
Exercise: If sin(θ + 180°) = -sin(θ), what trigonometric identity can be used to simplify this expression?
Video class: Reduction grade 11: practice03m
Exercise: Which trigonometric identity equation is equivalent to the expression: (-cos²x + 1) / (sin²x)?
Video class: Reduction grade 11: practice04m
Exercise: What is the simplified value of the expression cos(130°) + sin(400°) if you consider the properties of trigonometric functions and their respective quadrants?
Video class: Identities Grade 11: Introduction and practice25m
Exercise: What is the value of sin^2(θ) + cos^2(θ) for any angle θ?
Video class: Identities Grade 11: Practice03m
Exercise: In a trigonometric expression, you are tasked with simplifying tan²(x) - sin²(x) to one of the standard trigonometric identities. If you let tan(x) be represented as sin(x)/cos(x), what does the expression simplify to?
Video class: Identities Grade 11: Practice03m
Exercise: Which of the following trigonometric identities is correct?
Video class: Identities Grade 11: Practice03m
Exercise: Which of the following trigonometric expressions is equivalent to cot(x)?
Video class: Identities Grade 11: Practice02m
Exercise: When you simplify the expression (sin x / (1 + cos x)) + (1 / tan x), what will it become?
Video class: Identities Grade 11: Practice01m
Exercise: Which of the following expressions simplifies to 1 using trigonometric identities?
Video class: General and Specific Solution grade 11:Part 115m
Exercise: Solve the trigonometric equation \( \tan(x) = -\sqrt{3} \) for \( x \) in the interval \( [0, 360) \) degrees.
Video class: General and Specific Solution grade 11: Part 217m
Exercise: In solving the equation 2tan(x) = tan(x) + 3, what is the value of x in degrees for 0 ≤ x < 360?
Video class: General Solution Grade 11: Practice07m
Exercise: In a typical cosine graph, the function is undefined for certain values of d. Which of the following intervals represent the range of values where the function is defined?
Video class: General Solution Grade 11: Practice04m
Exercise: What is the value of sin(x) if you solve the equation 3sin²(x) + 5sin(x) - 2 = 0 using the quadratic formula?
Video class: General Solution Grade 11: Practice06m
Exercise: If sin(x) = cos(30° - x), what is the value of angle x?
Video class: General Solution Grade 11: Practice02m
Exercise: Given the equation: sin(a - 30) = sin(a), where a is in the interval [0, 360] degrees, find the general solution and specify the values of a within the given interval.
Video class: General Solution Grade 11: Practice02m
Exercise: What is the reference angle for the trigonometric expression when you perform an inverse sine operation on 0.4?
Video class: General Solution Grade 11: Practice02m
Exercise: Given that 3tan(x) = 2, what is the reference angle for x?
Video class: General Solution Grade 11: Practice04m
Exercise: Given the equation sin(x) - 2(1 - sin²(x)) + 2 = 0, what are the solutions for x in terms of k, where k is an integer?
Video class: Identities grade 1102m
Exercise: In trigonometry, when simplifying the expression \( \frac{2 \, \sin x}{1 - \sin^2 x} \), which identity can be directly applied to simplify the denominator?
Video class: Reduction grade 11: practice03m
Exercise: Simplify the following trigonometric expression as much as possible: sin(40°) × sin(x) / (cos(50°) × tan(x)).
Video class: Identities grade 1103m
Exercise: Given that sin²(x) + cos²(x) = 1, which of the following identities is correct?
Video class: Trigonometry Grade 11 Exam Question08m
Exercise: If a point T is located on the line segment OP where O is the origin and OP is 25 units long, and the coordinates of P are (-7, 24), what are the coordinates of T if OT is 15 units long?
Video class: Trigonometry Grade 11 Exam Question07m
Exercise: Simplify the trigonometric expression (sin^2(x) / (4 * cos(90° + x))) into a single trigonometric term.
Video class: Trigonometry Grade 11 Exam Question07m
Exercise: Consider a triangle on the Cartesian plane where point P is at (-7, 4). Using this triangle, what is the value of cos(θ) for θ being the angle at point P with reference to the horizontal? Assume the hypotenuse is calculated using Pythagoras' theorem.
Video class: General Solution Grade 11: Exam06m
Exercise: Determine the general solution for the equation cos(2x) = 0.
Video class: Trigonometry Grade 11 Exam Question04m
Exercise: In a triangle, angle α is such that tan(α) = -3/4. If angle α is in the second quadrant, what is the measure of angle α?
Video class: Reduction grade 11: Exam04m
Exercise: Given a trigonometric expression: -sin(30) * tan(30), what is the simplified result without using a calculator?
Video class: Identities grade 1101m
Exercise: What is the equivalent expression of \( \frac{\sin(x) (1 - \cos(x))}{\cos(x)} \)?
Video class: Grade 11 Trigonometry Exam Questions04m
Exercise: Simplify the following expression to a single trigonometric ratio, without using a calculator: (1 - sin² θ) / cos θ.
Video class: General Solution Grade 11 Exam Questions05m
Exercise: Solve the equation 3 tan(4X) = -2 cos(4X) for X and determine which solutions are valid.
Video class: Trigonometry Grade 11 Exam Questions04m
Exercise: What is the minimum value of the function f(x) = 1 - sin(x)?
This free course includes:
4 hours and 29 minutes of online video course
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
How do you use the CAST diagram to find cos θ when sin θ = 3/5 in quadrant II?
Use the 3-4-5 triangle: |cos θ| = 4/5. Cosine is negative in quadrant II, so cos θ = -4/5.
What is the reduction formula for sin(270° - x)?
sin(270° - x) = -cos x. The angle lies in quadrant III relative to the x-axis, where sine is negative.
How do you solve tan x = -√3 for 0° ≤ x < 360°?
The reference angle is 60°. Tangent is negative in quadrants II and IV, so x = 120° or 300°.
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