Trigonometric Functions of Allied Angles - Mathematics Class 11

Trigonometric function of allied angles:
Trigonometric ratios of Allied angles. Trigonometric ratios of allied angles, when the sum or difference of two angles is either zero or a multiple of 90 0 . ... The angles − Θ , 90 0 ± Θ , 360 0 ± θ etc. are angles allied to the angle Θ , if Θ is measured in degrees.

Trigonometric Functions:
The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Formula:
Sin(−θ)=−SinθSin(−θ)=−Sinθ
Cos(−θ)=CosθCos(−θ)=Cosθ
Tan(−θ)=−TanθTan(−θ)=−Tanθ
Sin(90∘−θ)=CosθSin(90∘−θ)=Cosθ
Cos(90∘−θ)=SinθCos(90∘−θ)=Sinθ
Tan(90∘−θ)=CotθTan(90∘−θ)=Cotθ
Sin(180∘−θ)=SinθSin(180∘−θ)=Sinθ
Cos(180∘−θ)=−CosθCos(180∘−θ)=−Cosθ
Tan(180∘−θ)=−TanθTan(180∘−θ)=−Tanθ
Sin(270∘−θ)=−CosθSin(270∘−θ)=−Cosθ
Cos(270∘−θ)=−SinθCos(270∘−θ)=−Sinθ
Tan(270∘−θ)=CotθTan(270∘−θ)=Cotθ
Sin(90∘+θ)=CosθSin(90∘+θ)=Cosθ
Cos(90∘+θ)=−SinθCos(90∘+θ)=−Sinθ
Tan(90∘+θ)=−CotθTan(90∘+θ)=−Cotθ
Sin(180∘+θ)=−SinθSin(180∘+θ)=−Sinθ
Cos(180∘+θ)=−CosθCos(180∘+θ)=−Cosθ
Tan(180∘+θ)=TanθTan(180∘+θ)=Tanθ
Sin(270∘+θ)=−CosθSin(270∘+θ)=−Cosθ
Cos(270∘+θ)=SinθCos(270∘+θ)=Sinθ
Tan(270∘+θ)=−CotθTan(270∘+θ)=−Cotθ




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