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Applications of trignometry
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The documents contains the information about Trigonometry and applications of trigonometry which is important topic for students who are preparing for engineering exams
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Applications of TrigonometryTrigonometry can help you find the height of a tall building like the Burj Khalifa without going to the top. Y
ou can also find the width of a river without using a long tape. Check out our video on heights and distanc
es for more information.
Pythagoras Theorem
Remember Pythagoras theorem which states that in a right angle triangle, the square of the hypotenuse i
s equal to the sum of the squares of the other two sides. This theorem is helpful in finding the third side of
a right angle triangle when given the other two sides.
Trigonometry Ratios
Trigonometry deals with right angle triangles and their angles and sides. In a right angle triangle, we have
the hypotenuse, perpendicular, and base. These terms are important in understanding the trigonometric r
atios. Given an angle and a side, we can use trigonometry to find the other sides and angles of the triangl
e.
Trigonometric Ratios in a Right Angle Triangle
In a right angle triangle, the longest side opposite to the 90-degree angle is called the hypotenuse. The si
de that contains the 90-degree angle and the angle theta is called the base, while the side opposite to the
angle theta is called the perpendicular.
Sine theta is defined as the ratio of perpendicular by hypotenuse, or AB/AC.
Cos theta is defined as the ratio of base by hypotenuse, or BC/AC.
Tan theta is defined as the ratio of perpendicular by base, or AB/BC.
It’s important to note that these ratios only apply to right angle triangles.
Reciprocal Ratios
There are also reciprocal ratios of the trigonometric ratios:
Cosecant (csc) theta is defined as the reciprocal of sine theta, or AC/AB.
Secant (sec) theta is defined as the reciprocal of cos theta, or AC/BC.
Cotangent (cot) theta is defined as the reciprocal of tan theta, or BC/AB.
Relation between Sine, Cosine, and Tangent
In a right angle triangle, sine, cosine, and tangent are related as follows:
Sine theta = perpendicular/hypotenuse = AB/AC
Cosine theta = base/hypotenuse = BC/AC
Tangent theta = perpendicular/base = AB/BC
Cosecant theta = hypotenuse/perpendicular = AC/AB
Secant theta = hypotenuse/base = AC/BC
Cotangent theta = base/perpendicular = BC/AB
It’s important to note that the hypotenuse is always opposite to the 90-degree angle, the base contains bo
th the 90-degree and theta angles, and the perpendicular is opposite to the theta angle.
Trigonometric Ratios: Explained and Solved
In trigonometry, we are interested in the relation between sine theta cos theta and tan theta. Let’s define t
hese terms:
Sine theta: Perpendicular by Hypotenuse
Cos theta: Base by Hypotenuse
Tan theta: Perpendicular by Base
The relation between these terms is that tan theta = sine theta / cos theta. This can be easily proven by ta
king the numerator (perpendicular by hypotenuse) and denominator (base by hypotenuse), which will can
cel out the hypotenuse and leave you with perpendicular by base, which is equal to tan theta. Similarly, co
t theta (reciprocal of tan theta) is equal to cos theta / sine theta.
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