Trigonometry

Sections

1. 7A Trigonometry with right-angled triangles Sine, cosine and tangent in a right-angled triangle, the exact values for 30°, 45° and 60°, the reciprocal ratios, and finding unknown sides and angles.
2. 7B Problems with right-angled triangles Solve practical problems using angles of elevation and depression, compass bearings and true bearings, drawing a clear diagram first.
3. 7C Trigonometric functions of a general angle Define sin, cos and tan for any angle using a point on a circle, find values at the boundary angles 0°, 90°, 180° and 270°, and meet the graphs, domains, periods and amplitudes.
4. 7D Quadrant, sign and related acute angle Use the ASTC rule and the related acute angle to find the exact value of sin, cos and tan of any angle, including negative angles and angles over 360°.
5. 7E Given one trigonometric function, find another Given one trig ratio and the quadrant, draw a triangle, use Pythagoras for the third side, and use ASTC to get the sign of every other ratio.
6. 7F Trigonometric identities The reciprocal, ratio, Pythagorean and complementary-angle identities, and how to simplify trig expressions and prove identities.
7. 7G Trigonometric equations Solve trig equations in a given domain: find the related angle, use ASTC to choose quadrants, handle boundary angles, compound angles and equations with two trig functions.
8. 7H The sine rule and the area formula Use the sine rule to find sides and angles in any triangle, watch for the ambiguous case, and find area with ½ab sin C.
9. 7I The cosine rule Use the cosine rule to find a side from two sides and the included angle, or an angle from three sides, and see how it extends Pythagoras' theorem.
10. 7J Problems involving general triangles Choose between the sine rule, cosine rule and area formula using the congruence tests, and solve two-step problems including bearings and heights.