3Blue1Brown
Derivative formulas through geometry | Essence of calculus, chapter 3
Introduction to the derivatives of polynomial terms and trigonometric functions thought about geometrically and intuitively. The goal is for these formulas to feel like something the student could have discovered, rather than something...
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Checking and securing understanding of cosine problems
Pupil outcome: I can use the cosine ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The cosine ratio involves the hypotenuse, adjacent and the angle - If you know the length of the hypotenuse...
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Problem solving with right-angled trigonometry
Pupil outcome: I can use my knowledge of right-angled trigonometry to solve problems. Key learning points: - Sometimes an answer may be best left in an exact form - When dealing with right-angled trigonometry, it is important to look at...
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Applying trigonometric ratios in context
Pupil outcome: I can apply trigonometric ratios to practical situations including angles of elevation and depression. Key learning points: - Trigonometric ratios are used in many scenarios - Trigonometric ratios are used to calculate the...
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Interpreting the trigonometric graphs
Pupil outcome: I can read values from the graphs and can identify how many solutions exist within a given range. Key learning points: - Reading solutions from trigonometric graphs is the same as reading solutions from any other graph -...
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Calculate trigonometric ratios for 30° and 60°
Pupil outcome: I can calculate trigonometric ratios for 30° and 60°. Key learning points: - The trigonometric ratios for 30° and 60° can be calculated using an equilateral triangle - The triangle should have lengths of 2 units - By...
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Advanced problem solving with right-angled trigonometry
Pupil outcome: I can use my knowledge of right-angled trigonometry to solve problems. Key learning points: - Sometimes an answer may be best left in an exact form - When dealing with right-angled trigonometry, it is important to look at...
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Problem solving with non right-angled trigonometry
Pupil outcome: I can use my knowledge of trigonometry to solve problems. Key learning points: - Non right-angled trigonometry can be applied in various contexts - It has the potential to be applied whenever a triangle can be drawn
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Checking and securing understanding of trigonometric ratios
Pupil outcome: I can appreciate the range of values of the trigonometric functions. Key learning points: - The unit circle is a circle with a radius of one - The unit circle is centered on the origin - The sine of an angle is the...
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Calculate trigonometric ratios for 0°, 45° and 90°
Pupil outcome: I can calculate trigonometric ratios for 0°, 45° and 90°. Key learning points: - The trigonometric ratios for 45° can be calculated using a square - The square should have lengths of 1 unit - By splitting the square into...
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Drawing the sine and cosine graphs
Pupil outcome: I can draw the graphs for the trigonometric functions sine and cosine. Key learning points: - The unit circle can help you predict what the graphs of the trigonometric functions will look like - The sine and cosine graphs...
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Using the cosine ratio
Pupil outcome: I can use the cosine ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The cosine ratio involves the hypotenuse, adjacent and the angle. - If you know the length of the hypotenuse...
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Using the tangent ratio
Pupil outcome: I can use the tangent ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The tangent ratio involves the opposite, adjacent and the angle. - If you know the length of the opposite and...
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Checking and securing understanding of tangent ratio problems
Pupil outcome: I can use the tangent ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The tangent ratio involves the opposite, adjacent and the angle - If you know the length of the opposite and...
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Checking and securing understanding of sine ratio problems
Pupil outcome: I can use the sine ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The sine ratio involves the hypotenuse, opposite and the angle - If you know the length of the hypotenuse and...
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Checking and securing understanding of the unit circle
Pupil outcome: I can see how the trigonometric functions are derived from measurements within a unit circle and how this can be utilised. Key learning points: - Trigonometric functions are derived from measurements within a unit circle -...
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The unit circle
Pupil outcome: I can appreciate that the trigonometric functions are derived from measurements within a unit circle. Key learning points: - The unit circle is a circle with a radius of one. - The unit circle is centered on the origin. -...
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Factoring Special Products 2
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Vertex Form Word Problems (Quadratics)
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Practice Problems - Arc and Angle Relationships
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Intro to Logs and Solving Log Equations
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Matrix Multiplication (same dimension)
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Graphing Rational Functions of Differing Degrees
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...
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Simplify Rational Expressions by Factoring
Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...