PROJECT ON TRIGONOMETRY

DESIGNED BY:AARTHEE A

AMIRTHA VARSHINI VHARINI RHEMA M

SUKEERTHI S

Sin θ

Cot θ

Cos θ

Cosecant θ

∟A

½=θ

TRIGONOMETRIC RATIOSLet us take a right angle ABC as shown in figure.Here, ∟CAB or ∟A is an acute angle. Note the position of side BC with respect to ∟A. It faces ∟A. we call it the side opposite to ∟A(perpendicular). AC is hypotenuse of the right angle and the side AB is a part of ∟A. so, we call it the side adjacent to ∟A(base).

The trigonometric ratios of the angle A in the right triangle ABC see in fig.

• Sin of A =side opposite to angle A =BC hypotenuse AC

• Cosine of A =side adjacent to angle A =AB hypotenuse AC

• Tangent of A =side opposite to angle A =BC side adjacent to angle A AB

C

A B

Cosecant of A = 1 = hypotenuse = AC

sin of A side opposite to angle A BCSecant of A = 1 = hypotenuse = AC

sin of A side adjacent to angle a ABCotangent of A= 1 =side adjacent to angle A= AB

tangent of A side opposite to angle A BC

C

A B

RECIPROCALS OF SIN , COS & TAN

Sin θ = reciprocal= Cosec θ

Cos θ = reciprocal = Sec θ

Tan θ = reciprocal = Cot θ

Means :-Sin θ = 1/ Cosec θ (sin θ * cosec θ =

1 )

Cos θ = 1/ Sec θ ( cos θ * sec θ = 1 )

Tan θ = 1/ Cot θ ( tan θ * cot θ = 1 )

VALUES OF TRIGONOMETRIC RATIOS∟θ 0° 30° 45° 60° 90°Sin θ 0 1/2 1/√2 √3/2 1Cos θ 1 √3/2 1/√2 1/2 0Tan θ 0 1/√3 1 √3 NOT

DEFINED

Cosec θ

NOTDEFINED 2 √2 2/√3 1

Sec θ 1 2/√3 √2 2 NOT DEFINED

Cot θ NOT DEFINED √3 1 1/√3 0

FORMULASSin ( 90° – θ ) = Cos θCos ( 90° – θ ) = Sin θ

Tan ( 90° – θ ) = Cot θ Cot ( 90° – θ ) = Tan θ

Cosec ( 90° – θ ) = Sec θ

Sec ( 90° – θ ) = Cosec θ

MAIN IDENTITIES Sin²θ + Cos² θ = 11 + Tan² θ = Sec² θ1 + Cot² θ = Cosec² θSinθ / Cos θ = Tan θCosθ / Sin θ = Cot θSin² θ / Cos² θ = Tan² θCos² θ / Sin² θ = Cot² θ

STEPS OF PROVING THE IDENTITIES

1)Solve the left hand side or right hand side of the identity.

2)Use an identity if required.3)Use formulas if required.4)Convert the terms in the form of sinθ

or cos θ according to the question.5)Divide or multiply the L.H.S. by sin θ

or cos θ if required.6)Then solve the R.H.S. if required.7)Lastly , verify that if L.H.S. = R.H.S.

THANK YOU