Trigonometry, Sine, Cosine and Tan

Trigonometry Ratios

  1. Sine, cosine and tangent with reference to right angled triangle

sine

 

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)

  1. Trigonometry I
  2. Derivation of trigonometric ratio of 30 degrees, 45 degrees and 60 degrees from drawn angless

Derivation of Tan, sin are cos 45o

Cosine

/AB/ = /BC/ = 1 unit

/AC/2 = 12 + 12 (Pythagoras theorem)

/AC/2 = 2

/AC/ = 2 units

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

A + C = 900   (sum of  angle of      )

A = C = 450

tan 400 = opp = 1/1 = 1

adj

sin 450 = opp => 1__

adj

 

cos  450 adj => 1__

hyp

Tan, sin and cos 600 and 300

Tan

/BC/ = /DC/ = 1 UNIT

In    ABC

/AB/2 = /AD/2 + /AD/2 (Pythagoras theorem)

22 = /AD/2 + 12

/AD/2 = 22 – 12 = 4 -1

= 3

:. /AD/ =  units

Sin B = 600

Tan 600 = √3⁄1 = √3

Sin 600 =√3⁄2

Cos 600 = ½

 

For 300

Tan 300 = 1 ⁄√3

 

Sin 300 = ½

Cos 300 = √3⁄2

  1. Trigonometry I
  2. Angle of elevation and depression
  3. Application of trigonometric ratio

 

  1. Trigonometric Ration I
  2. In relation to unit circle, sine and cosine of various angles

 

 

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

 

  1. Length of Arc of circles

Depth of arc

Circle

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

Circle 2

Length of an arc PQ = 360 x 2

84 x 2 x 22 x 7

300         7

 

84 x 11 = 10.3cm

90

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