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SOHCAHTOA BY: KAYLA SLEDGE

Example

Pythagorean Theorem

The longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle:

the square of the hypotenuse is equal to

the sum of the squares of the other two sides.

a2 + b2 = c2

92 + b2 = 152

81 + b2 = 225

Take 81 from both sides:

b2 = 144

b = √144

b = 12

Inverse of Sine, Cosine, and Tangent

First, regardless of how you are used to dealing with exponentiation we tend to denote an inverse trig function with an “exponent” of “-1”. In other words, the inverse cosine is denoted as

cos a° = Adjacent / Hypotenuse

cos a° = 6,750/8,100 = 0.8333...

a° = cos-1 (0.8333...) = 33.6° (to 1 decimal place)

It is important here to note that in this case the “-1” is NOT an exponent and so,

tan x° = Opposite / Adjacent

tan x° = 300/400 = 0.75

x° = tan-1 (0.75) = 36.9° (correct to 1 decimal place)

Start with: sin a° = opposite/hypotenuse = 18.88/30

Calculate 18.88/30: sin a° = 0.6293...

Inverse Sine: a° = sin-1(0.6293...)

Use a calculator to find sin-1(0.6293...): a° = 39.0° (to 1 decimal place)

The angle "a" is 39.0°

Example

SOHCOHTOA

SOH - stands for Sine equals Oppisite over Hypotenuse

COH - stands for Cosine equals Adjacent over Hypotenuse

TOA - stands for Tangent equals Opposite over Adjacent

sin θ = 3/5 = 0.6

cosθ = 4/5 = 0.8

tanθ = 3/4 = 0.75

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