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Summary Trigonometry, Advanced Programme Mathematics - Grade 12 (IEB) $2.81   Add to cart

Summary

Summary Trigonometry, Advanced Programme Mathematics - Grade 12 (IEB)

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Covers the various sections relating to Trigonometry within the Advanced Mathematics programme. Includes notes from the textbook, as well as additional class, video and research information, diagrams and practice questions. Applicable to all IEB Grade 12s.

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  • February 15, 2021
  • 7
  • 2020/2021
  • Summary
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Trigonometry
Ratios:

Co-ratio Triangle Name Variables Inverse
cos θ 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 sin θ 𝑦 cosec θ
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑟
sin θ 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 cos θ 𝑥 sec θ
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑟
cot θ 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 tan θ 𝑦 cot θ
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑥
sec θ ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cosec θ 𝑟 sin θ
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑦
cosec θ ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sec θ 𝑟 cos θ
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑥
tan θ 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 cot θ 𝑥 tan θ
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑦

Identities:

1. Quotient
𝑠𝑖𝑛𝜃
tan θ = 𝑐𝑜𝑠𝜃

2. Inverse
1
sin θ =
𝑐𝑜𝑠𝑒𝑐𝜃
1
cos θ = 𝑠𝑒𝑐𝜃
1
tan θ = 𝑐𝑜𝑡𝜃

3. Square
cos2x + sin2x = 1
1 + cot2x = cosec2x
1 + tan2x = sec2x
Reduction formula:



90° + Ɵ 90° - Ɵ

180° - Ɵ 360° + Ɵ




180° + Ɵ 360° - Ɵ - Ɵ

270° - Ɵ 270° + Ɵ

, Radian Measure
Radian measure of an angle is the ratio of the 2 lengths, measures in the same units and is thus
a pure number. (has no unit)
One radian is defined as = the angle subtended at the centre of a circle by an arc equal in
length to the radius of the circle

b
r
θ S
r
a

𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑆
θ= 𝑟𝑎𝑑𝑢𝑖𝑠
= 𝑟

S = θr radius

Angle in radians

Arc length

Notations: 1 radian is written as 1 rad
180°
Radian to Degrees: x 𝜋
𝜋
Degrees to Radian: x 180°


Special angles in radian:
𝜋
30° = 6
𝜋
45° = 4
𝜋
60° =3
𝜋
90° =2
180° = π
360° = 2 π


sin θ and
cosec θ are All positive
positive




tan θ and cos θ and
cot θ are sec θ are
positive positive

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