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Learn: Introduction to Trigonometry
iGCSE Mathematics
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Welcome!Today we'll explore the basics of trigonometry. By the end of this lesson, you'll understand how to use trigonometric ratios to solve problems involving triangles. Let's dive in!
What is Trigonometry?Trigonometry is the study of the relationships between the angles and sides of triangles. It is particularly useful for solving problems involving right-angled triangles, such as calculating distances or heights.
Right-Angled TrianglesA right-angled triangle is a triangle where one of the angles is 90°. It has three sides: the hypotenuse (the longest side opposite the right angle), the opposite side (opposite the angle of interest), and the adjacent side (next to the angle of interest).
Which side of a right-angled triangle is always the longest?
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Trigonometric RatiosTrigonometric ratios link the angles and sides of a right-angled triangle. These ratios are sine (sin), cosine (cos), and tangent (tan). They are defined as:sin θ = opposite/hypotenusecos θ = adjacent/hypotenusetan θ = opposite/adjacentThese ratios are used to find missing side lengths or angles in right-angled triangles.
Using Sine, Cosine, and TangentTo solve a triangle, first identify the angle you are working with, then determine which sides are the opposite, adjacent, or hypotenuse. Select the appropriate trigonometric ratio based on the sides you know and want to find.
The formula for tan θ is {{blank0}} divided by {{blank1}}.
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Finding Unknown SidesTo find unknown side lengths, use the trigonometric ratios. Rearrange the formula to solve for the missing side.For example, if you know the angle θ and the hypotenuse, and need to find the opposite side, use the formula: opposite = sin θ × hypotenuse.
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Finding Unknown AnglesYou can also find an unknown angle using trigonometric ratios. For example, if you know the opposite and adjacent sides, use the formula: tan θ = opposite/adjacent. Then use the inverse tangent function (tan-1) to find the angle.
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Exact Values for Special AnglesFor certain angles, trigonometric values are exact and easy to remember. For example:sin 30° = 0.5cos 45° = √2/2tan 60° = √3These values are often required for calculations in iGCSE Mathematics.
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Review Time!Fantastic work! You've learned about trigonometric ratios, how to find unknown sides and angles, and exact values for special angles. Now let's test your understanding!
Which trigonometric ratio is used to find an angle when given the opposite and adjacent sides?
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Which of the following are exact trigonometric values? (Select all that apply)
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Well Done!You've completed the lesson on trigonometry! Keep practising to master these concepts, and you'll be solving triangles like a pro in no time.
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