Trigonometry for Cambridge IGCSE/GCSE Mathematics 0580 Exam

Explore the basics of trigonometry in right triangles, defining sine, cosine, and tangent as the ratios of opposite, adjacent, and hypotenuse. Use soh cah toa mnemonic to remember these relationships.

Learn how to find unknown sides in right triangles using sine, cosine, and tangent, and obtain results correct to three significant figures, with step-by-step examples and calculator guidance.

Apply tan 32°, sin 38°, cos 40°, and sin 28° in a sequence of right triangles to find BD, then x, then y.

Identify unknown angles in right triangles by applying sine, cosine, or tangent to opposite, adjacent, and hypotenuse, using inverse functions on a calculator to obtain degrees.

Learn to find unknown angles in right triangles using tan, sine, and cosine, by solving for missing sides and applying opposite, adjacent, and hypotenuse relationships through worked examples.

Apply the sine rule to find unknown sides or angles in non-right triangles, using a/sin A = b/sin B = c/sin C with a known side and its opposite angle.

Apply the sine rule in triangles when a side and its opposite angle are known, and use angle-sum property to find angles, with obtuse-angle examples using sin(180 degrees minus theta).

Use the cosine rule to find missing sides or angles from two sides with the included angle, or from all three sides; convert obtuse angles to acute for calculators.

Apply the cosine rule to find missing sides from two sides and the included angle, handling acute and obtuse cases with calculator precision.

Use the cosine rule to find unknown angles in triangles from given side lengths, compute cos values and inverse cos, and identify obtuse angles in multiple example problems.

Learn how bearings are defined as angles measured clockwise from north, written in three digits, and how to find bearings between points using north arrows, corresponding angles, and 180-degree relationships.

Resolve ship travel from bearings by decomposing 35 km at 42 degrees into north and east via cosine and sine, and 200 km at 243.7 degrees into south and west.

Apply sine to a right triangle with a 6 m ladder and 2 m from wall to find 19.5°, then compute 8 m ladder base at 31° as 4.12 m.

solves a bearings problem by using tan ratios in several right triangles to find missing lengths, then computes final distance d as 8.6 m.