3.1 Geometry and trigonometry - SL content

• Use distance and midpoint in three-dimensional space.

• Use volume and surface area of common 3D solids and combinations.

• Identify right-angled triangles in 3D objects to find lengths and angles.

• Use sine, cosine and tangent in right-angled triangles.

• Use sine rule, cosine rule and area formula 1/2 ab sin C.

• Ambiguous sine-rule case is not included here.

• Apply right and non-right triangle trigonometry, including Pythagoras' theorem.

• Use angles of elevation/depression and bearings; construct labelled diagrams from text.

• Use radians for angles.

• Find arc length and sector area; express radians exactly with pi or as decimals.

• Define sin theta and cos theta using the unit circle; tan theta=sin theta/cos theta.

• Use quadrant relationships and exact trig values for standard angles.

• Include ambiguous sine-rule case.

• Use cos^2 theta + sin^2 theta = 1.

• Use double-angle identities for sine and cosine.

• Use trig-ratio relationships without necessarily finding the angle.

• Graph sin x, cos x and tan x with amplitude and periodicity.

• Use transformations of a sin(b(x+c))+d in degrees or radians.

• Apply to contexts such as tides and Ferris wheels.

• Solve trigonometric equations on finite intervals graphically and analytically.

• Include equations reducible to quadratics in sin x, cos x or tan x.

• General trig solutions are not required.