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Pipeng : Maths Trigonometry : Triangles Sine Cosine And Tangent ALPHA Maths Homework Module

Triangles ALPHA Maths Module

Description : Maths Trigonometry : Triangles Sine Cosine And Tangent

Tools In This Module:

ALPHA : Trigonometry : Angles 11 : Angle Sine : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 12 : Angle Cosine : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 13 : Angle Tangent : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Triangles 01 : Pythagorus Formula : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Triangles 02 : Triangle Sine Rule : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Triangles 03 : Triangle Cosine Rule : ALPHA Maths Homework Exercise


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Module List

ALPHA : Trigonometry : Angles 11 : Angle Sine : ALPHA Maths Homework Exercise

Description : Angle sine.

Discussion : The sine is the ratio of the vertical component over the radius. See figure Angle Sine Cosine And Tangent

The homework exercise has 4 questions.

sine
radius
vertical component
angle

The equations are :

s = sind(theta) = y / r
r = y / s = y / sind(theta)
y = r sind(theta)
theta = asind(y / r)

where

theta = angle
r = radius
y = vertical component
s = sine

Note : Angles are in degrees. Use the degree trig functions sind() and asind().

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ALPHA : Trigonometry : Angles 12 : Angle Cosine : ALPHA Maths Homework Exercise

Description : Angle cosine.

Discussion : The cosine is the ratio of the horizontal component over the radius. See figure Angle Sine Cosine And Tangent

The homework exercise has 4 questions.

cosine
radius
vertical component
angle

The equations are :

c = cosd(theta) = x / r
r = x / c = x / cosd(theta)
x = r * cosd(theta)
theta = acosd(x / r)

where

theta = angle
r = radius
x = horizontal component
c = cosine

Note : Angles are in degrees. Use the degree trig functions cosd() and acosd().

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ALPHA : Trigonometry : Angles 13 : Angle Tangent : ALPHA Maths Homework Exercise

Description : Angle tangent.

Discussion : The tangent is the ratio of the vertical component over the horizontal component. See figure Angle Sine Cosine And Tangent

The homework exercise has 4 questions.

tangent
radius
vertical component
angle

The equations are :

t = tand(theta) = y / x
x = y / t
y = x tand(theta)
theta = atand(y / x)

where

theta = angle
y = vertical component
x = horizontal component
t = tangent

Note : Angles are in degrees. Use the degree trig functions tand() and atand().

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ALPHA : Trigonometry : Triangles 01 : Pythagorus Formula : ALPHA Maths Homework Exercise

Description : Pythagorus formula.

Discussion : From Pythagorus's formula the square of the hypotenuse of a right angled triangle equals the sum of the squares of the other two sides. See figure Right Angle Triangle Dimensions And Angles

The homework exercise has 2 questions.

hypotenuse
side

The equations are :

c = √(a2 + b2)
a = √(c2 - b2)

where

a b c = sides of right angled triangle (c = hypotenuse)

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ALPHA : Trigonometry : Triangles 02 : Triangle Sine Rule : ALPHA Maths Homework Exercise

Description : Triangle sine rule.

Discussion : According to the triangle sine rule the ratio of the side over the sine of the opposite angle is constant for all sides and angles. See figure Triangle Dimensions And Angles

The homework exercise has 2 questions.

side a
angle A

The equations are :

a / sind(A) = b / sind(B) = c / sind(C)
a = b sind(A) / sind(B)
A = asind(sind(B) a / b)

where

a b c = sides of triangle
A B C = opposite angles of triangle

Note : Angles are in degrees. Use the degree trig functions sind() and asind().

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ALPHA : Trigonometry : Triangles 03 : Triangle Cosine Rule : ALPHA Maths Homework Exercise

Description : Triangle cosine rule.

Discussion : The cosine rule can be used to calculate one of the triangle angles if all three sides are known. See figure Triangle Dimensions And Angles

The homework exercise has 2 questions.

side a
angle A

The equations are :

a2 = b2 + c2 - 2 b c cosd(A)
a = √(b2 + c2 - 2 b c cosd(A))
A = acosd((b2 + c2 - a2) / (2 b c))

where

a b c = sides of triangle
A B C = opposite angles of triangle

Note : Angles are in degrees. Use the degree trig functions cosd() and acosd().

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