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Basics of Trigonometry

BASIC TRIGONOMETRY
180° = radians


sin θ = P / h
cos θ = b / h
tan θ = P / b



P – perpendicular ; h – hypotenuse  ;  b –base;



Standard Trignonometric Relations
...


sin2 θ + cos2 θ = 1
1+ tan2 θ =sec2 θ
1 + cot2 θ = cosec2 θ
-1 ≤ sin θ ≤ 1
-1 ≤ cos θ ≤ 1
sin θ = 1 / cosec θ
cos θ = 1 / sec θ
tan θ = 1 / cot θ


 
VALUES OF IMPORTANT TRIGONOMETRIC RATIOS

Θ
30°
45°
60°
90°
sin θ
0
1/2
1/√2
√3 / 2
1
cos θ
1
√3 / 2
1/√2
1/2
0
tan θ
0
1 / √3
1
√3


SIN
+
ALL
+

TAN
+
COS
+


Example - The angle of elevation of top of a tower from a point 240m from its foot is 30°. What is the height of the tower ?
Answer – tan θ = P / B = P / 240
tan 30° = P / 240

1 / √3 = P / 240
P = 240 / √3  = 80 √3 m
TRY THESE Questions
Question– Find the longest side of the right angled triangle which has its base as 20 and the acute angle is 45°

Question – The lamp post is 50 m away from a man whose height is 185cm. The height of lamp post is 10m. Find the length of the shadow of man?

Question – A man is standing 40 m from wall which is 30 m high. 10m behind the wall is a big tree.  The length tree visible to man is 10m. What is the total height of the tree?

Question – A tree 40 m away from the wall, fell on the wall and its tip just touched the topmost point of the wall while its roots were not uprooted. What could be the possible height of the tree? Height of Wall is 30m.


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1 comment:

  1. Here is some of the basic information about Trigonometry which I want to share with everyone, Its that branch of mathematics which is used to deal with the relationships between the sides and angles of triangles and the calculations based on them, specifically the trigonometric functions.types of angle

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