Exam-Focused Trigonometry Cambridge GCSE/IGCSE 0580 Extended

Master basic trigonometry by learning sine, cosine, and tangent with their reciprocals—cosecant, secant, cotangent—and soh cah toa definitions: opposite over hypotenuse, adjacent over hypotenuse, and opposite over adjacent.

Apply soh cah toa to compute sine, cosine, and tangent for angles in right triangles. Use opposite, adjacent, and hypotenuse to identify ratios, and apply Pythagoras to find missing sides.

Apply trigonometric ratios to find triangle sides in right triangles, using tangent, sine, and cosine with given angles and sides to compute opposite, adjacent, and hypotenuse lengths.

Use tan, sin, and cos to find sides in right triangles, derive BD from 32 degrees and 10 cm, then x and y as 13.1 cm and 27.9 cm.

Apply sine, cosine, and tangent to find x, y, and z in right triangles, using opposite, adjacent, and hypotenuse relationships and calculator accuracy to three significant figures.

Master trigonometry with right triangles by solving for x, y, and z using tan and sine with angles 40°, 50°, and 30°.

Apply trigonometry to find AB, BD, and CD in right triangles from AD = 20 cm, using tan 41°, cos 41°, and sine 35°.

Explore finding unknown angles in right triangles by using sine, cosine, and tangent with opposite, adjacent, and hypotenuse, and apply inverse trig to compute the angle in degrees.

Learn to find unknown angles in right triangles using tan, sine, and cosine with step-by-step worked examples that solve for missing sides and angles.

Learn to find an unknown angle in a right triangle by applying cosine and sine to two sub-triangles, compute sides y, z, BD, and obtain x at 54.8 degrees.

Apply the sine rule to find unknown sides or angles in non-right triangles, using a/sin A = b/sin B = c/sin C, including obtuse-angle handling and sample calculations.

Apply the sine rule by ensuring a known side and its opposite angle, use angle sum to find unknown angles, and solve for unknown sides, including obtuse cases.

Master the sine rule to find unknown angles and sides in triangles, using the sine formula and angle sum properties, with worked examples solving for x and y.

Use the sine rule to find unknown angles. First determine angle a from the opposite side and BC, then apply the angle-sum to obtain x, including obtuse cases.

Master the cosine rule to find missing sides or angles from two sides and the included angle, or from all three sides, and handle obtuse angles via supplementary angles.

Apply the cosine rule to determine missing sides from two sides and the included angle, handling acute and obtuse cases with calculator-assisted accuracy to three significant figures.

Learn to use the cosine rule to find an angle x in triangles from given side lengths, with examples showing obtuse results and cos inverse calculations.

Use the cosine rule to find missing angles and sides in triangles; calculate z as 60.2° and q as 1.40 cm, including handling an obtuse angle.

Learn how bearings are measured clockwise from north, written as three-digit numbers, and solved using north arrows, linear pairs, and 360-degree circles.

Use bearings and sine and cosine to find north/east from 35 km at 42°, and south/west from 200 km at 243.7°.

Apply sine to relate opposite and hypotenuse in a right triangle to find the angle between the ladder and the wall and the base distance from the wall.

apply trigonometry to bearings problems in right triangles, calculating y from 7 m with tan 40°, then x from 10 m, and finally determine d from BD and BC components.

Compute the ship's path from bearings. Use cosine and sine to find distances, then apply Pythagoras and tan to obtain AB 47.6 km and bearing from A 69.9 degrees.

Compute the north and east components from O for bearings 25° and 80°, then find OB and the bearing of B using sine, cosine, and Pythagoras.

Use the cosine rule to find distance from the starting point and bearing to the final position after two legs with bearings 100° and 160°, giving 954 km and 133°.

Apply trigonometry to bearings by plotting points, forming right triangles, and computing angles between a line ab and the x axis using tangent ratios and tan inverse.

Compute angles from coordinates using the distance formula and cosine rule with bearings examples, plotting points A, B, C and P, Q, R on a plane.

Apply bearings from a 75 m tower and use angles of depression 10° and 17° to determine distance between two goats, with cosine and sine rules illustrated in isosceles problems.

Apply the sine rule to find the circle radius of 9.51 cm. Then use Pythagoras and cosine rule to find the acute angle 71.1 degrees.

Apply sine and cosine to bearings problems: find string length from a 55° angle and height of kite from a 150 m line, and compute rocket height from vertical angles.

Determine angle x in a bearings-based trigonometry problem by using an isosceles trapezium, forming a parallelogram, and applying cosine and sine in right triangles derived from an equilateral triangle.

Solve bearing and trigonometry problems using right triangles, cosine and tangent ratios, to find distances, widths, and heights from angle of elevation examples.

Compute ac, diagonal of the 6 by 8 base, via Pythagoras to 10 cm, then find the angle between wc and ac using tan theta aw/ac, giving 16.7 degrees.

Compute the rectangular box diagonals using Pythagoras to find AC and r, then determine the angle between AC and r.

Apply three-dimensional trigonometry to a vertical pole in a rectangular field: compute height from A's 22-degree elevation, then determine angle at C, diagonal, and angle at D.

Calculate base diagonal BD and the diagonal BS of a 6 cm cube, then apply Pythagoras, tan, and cosine rule to find angles theta and alpha around 35.3°.

Explore a square-based pyramid by calculating the diagonal AC, the height, and angles such as the angle between VC and the base and angle ABC using Pythagoras and cosine rules.

Apply Pythagoras and trigonometry to a three-dimensional wedge: compute BS and AS, then find angles BSR, AR, and PAS using tan and cosine rules.

Explore three-dimensional trigonometry by calculating the space diagonal of a 4×6×8 cm box and its angle to the base diagonal, using Pythagoras and tangent.

Explains three-dimensional trigonometry using tangent to express AO and BO in terms of h from elevations 25° and 33°, then uses Pythagoras with AB = 60 m to find h.

Solve a three-dimensional trigonometry problem to find the tower height using angles of elevation from points south and east, with ab = 50 m, yielding about 22.6 m.

Use angles of depression from a 15 m tower to locate two men west and south, then apply tangent and Pythagoras to find their distance AB.

From points east and south, use elevation angles 27° and 11°, relate base distances via tan, and with AB = 40 m apply Pythagoras to find tower height 7.3 m.

Compute the angle vmb in a triangular pyramid with base ab=bc=15 cm and vb=10 cm, using pythagoras to find ac and bm, then tangent to get theta about 43.3 degrees.

Explore the unit circle, a radius-one circle at the origin, to relate coordinates (cos theta, sin theta) to trig ratios and tan theta equals sin theta over cos theta.

learn to plot the sine graph from 0 to 360 degrees using unit circle values, quadrant signs, zeros at 0, 180, 360, and its repeating pattern from -1 to 1.

Plot y = cos x from 0 to 360 degrees using key angles and quadrant signs. Cos x values range from 1 to -1, positive in first and fourth quadrants.

Draw the tangent graph y = tan x from 0 to 360 degrees, noting undefined at 90 and 270, quadrant signs, and the vertical asymptotes with infinite range.

Explore trig graphs, focusing on the sine wave, and learn to find alternate angles with the same sine value using the sine graph's symmetry. Examples include 18° and 162°.

Explore how cosine values occur at two angles on a graph and use symmetry to find pairs such as 70 and 290 degrees, and 160 and 200 degrees.

Explore identifying angles with the same tangent value on trig graphs. Use given values at 36° and 112° to find corresponding angles 216° and 292° by adding 180°.

Solve sin x = sqrt(3)/2 and cos x = 0.9 in 0-360 degrees; find 60°, 120°, 25.8°, and 334.2° using non-calculator and calculator methods.

Explore solving trig equations in 0 to 360 degrees using inverse trig and symmetry, with tan x = 0.5, cos x = -√2/2, sin x = -0.75, tan x = -6.

Solve 2 sin x = 1, 3 cos x = 2, 2 tan x = 7, and 1 + 3 sin x = 0 for 0–360 degrees using symmetry.

Learn to solve trigonometric equations in the 0-360 degree range using cos, sin, and tan, with tan inverse and symmetry about 180 degrees.

Learn exact trigonometric values for sine, cosine, and tangent at 0, 30, 45, 60, and 90 degrees without a calculator, in GCSE maths.

Derive sine, cosine and tangent values for angles using a right triangle and Pythagoras. Learn sin 45 = cos 45 = one divided by root two; tan 45 = one.

Learn to solve trig equations using exact values without calculators. Apply quadrant sign rules and theta forms to find all sine, cosine, and tangent solutions.

Learn to solve trigonometric equations without graphs by using a calculator to find inverse values and generate solutions in 0–360 degrees, using quadrant rules for sine, cosine, and tangent.