Trigonometry
Trigonometry for IB Applications and Interpretation SL: right triangles, sine and cosine rules, area, elevation and depression, with IB exam questions.
Trigonometry lets you calculate unknown sides and angles of a triangle from other sides and angles you already know. In this topic you revise the basics (Pythagoras, similarity, arcs and sectors), use sine, cosine and tangent in the right-angled triangle, solve any triangle with the sine and cosine rules, and calculate its area. In the Applications and Interpretation exam, almost every problem is a real situation (a ladder, a cliff, a plot of land, a balloon, a roof) with a diagram, and you solve it with the graphic display calculator (GDC). So what matters most is choosing the right tool and checking that the calculator is in degree mode.
Recommended order
Follow the sections in order: section 1 revises what you need, section 2 is the base of the topic (the right-angled triangle, angles of elevation and depression), section 3 covers the triangles that are not right-angled and section 4 adds area. At the end you have the IB exam questions grouped by type.
Pythagoras and proportionality from ESO (lower secondary), and topic 1 of this course (equations and approximation).
Sections in this topic
Prior knowledge: Pythagoras, similarity, arcs and sectors
Revise Pythagoras, similar triangles, degrees and minutes, arc length and sector area, with worked examples. IB Applications and Interpretation SL.
3 worked examples Section 2Trigonometric ratios in the right-angled triangle
Sine, cosine and tangent: find sides and angles of right-angled triangles, with elevation, depression and diagram problems. IB Applications SL.
3 worked examples Section 3Solving any triangle: sine and cosine rules
Sine rule and cosine rule: when to use each, the ambiguous case and problems with non-right-angled triangles. IB Applications and Interpretation SL.
3 worked examples Section 4Area of a triangle
How to find the area of a triangle with ½·a·b·sin C, find the included angle and measure plots of land. IB Applications and Interpretation SL.
3 worked examples End of topicIB exam questions for topic 3
IB exam questions on trigonometry: right triangles, sine and cosine rules, triangle area and combined problems, by type and level, with step-by-step solutions.
64 exercises · 25 ★★★ levelStuck on this topic?
Tell us where you get lost and we will tell you how to tackle it. Álvaro replies on WhatsApp.
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