CBSE Class 10 Application of Trigonometry Important Formulas and concepts for exams

CBSE Class 10 Application of Trigonometry Important Formulas and concepts for exams. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

Class 10 Maths Chapter 9 Some Applications to Trigonometry important formulas and concepts for CBSE exams. This page covers the angle of elevation and angle of depression, the trigonometric ratios of an acute angle in a right triangle, reciprocal and quotient relations, complementary angle identities and the table of trigonometric ratios for 0°, 30°, 45°, 60° and 90°.

ANGLE OF ELEVATION

In the figure, the line AC drawn from the eye of the student to the top of the minar is called the line of sight. The student is looking at the top of the minar. The angle BAC, so formed by the line of sight with the horizontal, is called the angle of elevation of the top of the minar from the eye of the student. Thus, the line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

[Figure: Left diagram shows a tall minar with its top marked C, the eye of the student at point A on the ground, the line of sight drawn from A to C (labelled Line of sight), the horizontal line AE, and the point B at the base of the minar with point D below it. The angle at A between the line of sight and the horizontal is marked Angle of elevation. Right diagram shows a person looking up at an object with the Line of sight, the Angle of elevation and the Horizontal level labelled.]

The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object.

ANGLE OF DEPRESSION

In the figure, the girl sitting on the balcony is looking down at a flower pot placed on a stair of the temple. In this case, the line of sight is below the horizontal level. The angle so formed by the line of sight with the horizontal is called the angle of depression. Thus, the angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed.

[Figure: A girl on a balcony looks down at an object on the ground. The horizontal level is a dashed line from the girl's eye. The angle between the horizontal level and the line of sight is marked Angle of depression. The line of sight runs from the girl's eye down to the object, which is labelled Object.]

Trigonometric Ratios (T - Ratios) of an acute angle of a right triangle

In XOY-plane, let a revolving line OP starting from OX trace out angle XOP = θ. From P (x, y), draw PM ⊥ OX.
In right angled triangle OMP, OM = x (Adjacent side); PM = y (Opposite side); OP = r (Hypotenuse).

[Figure: Coordinate axes with x and x' on the horizontal line and y and y' on the vertical line. The point P(x, y) is in the first quadrant. The segment OP is the hypotenuse marked r, the angle at O is marked θ, the perpendicular PM is marked y, and the base OM is marked x.]

sin θ = Opposite Side / Hypotenuse = y / r
cos θ = Adjacent Side / Hypotenuse = x / r
tan θ = Opposite Side / Adjacent Side = y / x
cosec θ = Hypotenuse / Opposite Side = r / y
sec θ = Hypotenuse / Adjacent Side = r / x
cot θ = Adjacent Side / Opposite Side = x / y

Reciprocal Relations

cosec θ = 1 / sin θ, sec θ = 1 / cos θ and cot θ = 1 / tan θ

Quotient Relations

tan θ = sin θ / cos θ and cot θ = cos θ / sin θ

Trigonometric ratios of Complementary angles

sin (90 - θ) = cos θ
tan (90 - θ) = cot θ
sec (90 - θ) = cosec θ
cos (90 - θ) = sin θ
cot (90 - θ) = tan θ
cosec (90 - θ) = sec θ

Trigonometric ratios for angles of measure 0°, 30°, 45°, 60° and 90° in tabular form