Trigonometry Ratios

- Sine, cosine and tangent with reference to right angled triangle

ABC is any triangle, right angle from SOH CAH TOA

Tan B=^{b}/_{c} (tan ^{opp}/_{adj})

Sin B = ^{b}/_{a} (Sin ^{opp}/_{hyp})

Cos B = ^{c}/_{a} (Cos ^{adj}/_{hyp})

- Trigonometry I
- Derivation of trigonometric ratio of 30 degrees, 45 degrees and 60 degrees from drawn angless

Derivation of Tan, sin are cos 45^{o}

/AB/ = /BC/ = 1 unit

/AC/^{2} = 1^{2} + 1^{2} (Pythagoras theorem)

/AC/^{2} = 2

/AC/ = 2 units

:. /AB = /BC/, A = C (Isosceles )

A + C = 90^{0} (sum of angle of )

A = C = 45^{0}

tan 40^{0} = __opp__ = ^{1}/_{1} = 1

adj

sin 45^{0} = __opp __=> __1____

adj

cos 45^{0} __adj __=> __1____

hyp

Tan, sin and cos 60^{0} and 30^{0}

/BC/ = /DC/ = 1 UNIT

In ABC

/AB/^{2} = /AD/^{2} + /AD/^{2} (Pythagoras theorem)

2^{2} = /AD/^{2} + 1^{2}

/AD/^{2} = 2^{2} – 1^{2} = 4 -1

= 3

:. /AD/ = units

Sin B = 60^{0}

Tan 60^{0} = √3⁄1 = √3

Sin 60^{0} =√3⁄2

Cos 60^{0} = ½

For 30^{0}

Tan 30^{0} = 1 ⁄√3

Sin 30^{0} = ½

Cos 30^{0} = √3⁄2

- Trigonometry I
- Angle of elevation and depression
- Application of trigonometric ratio

- Trigonometric Ration I
- In relation to unit circle, sine and cosine of various angles

- Graph of sines and cosine
- Using 15 degreed, 20 degrees, 30 degrees, 60 degrees etc.

- Length of Arc of circles

Depth of arc

Length of arc PQ = /_{360} x 2

e.g. Find the length of an arc of 9 circle of radius 7cm which subst an angle at the centre of the circle

Length of an arc PQ = _{360} x 2

__84__ x 2 x __22__ x 7

300 7

__84 x 11__ = 10.3cm

90