Question

in angle ABC angle B 5cm if AC 5cm BC 3cm AB 4cm find all the six trigonometric identities related to angle A​

Answer 1

Step-by-step explanation:

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Answer 2

Appropriate Question :-

In triangle ABC, is right angled at B. If AC = 5cm, BC = 3cm and AB = 4cm. Find all the six trigonometric identities related to angle A.

Answer :-

★ FIGURE

• Refer the attachment.

Firstly, we know, There are six trigonometric identities :-

$\sf{sine (sin \: A ) = \dfrac{Perpendicular}{Hypotenuse} \implies \dfrac{BC}{AC}}$

$\sf{cosine (cos \: A) = \dfrac{Base}{Hypotenuse} \implies \dfrac{AB}{AC}}$

$\sf{tangent (tan \: A) = \dfrac{Perpendicular}{Base} \implies \dfrac{BC}{AB}}$

$\sf{cotangent (cot \: A) = \dfrac{Base}{Perpendicular} \implies \dfrac{AB}{BC}}$

$\sf{secant (sec \: A) = \dfrac{Hypotenuse}{Base} \implies \dfrac{AC}{AB}}$

$\sf{cosecant (cosec \: A ) = \dfrac{Hypotenuse}{Perpendicular} \implies \dfrac{AC}{BC}}$

We have, Given

• AC = 5cm
• BC = 3cm
• AB = 4cm

∴ According the question,

• sine ( sin A )

$\sf{ \longrightarrow \: sine (sin \: A ) = \dfrac{BC}{AC}}$

$\sf{ \longrightarrow \: \dfrac{BC}{AC}}$

$\sf{ \longrightarrow \: \dfrac{3}{5} \: \: \: \: \bigstar}$

• cosine ( cos A )

$\sf{ \longrightarrow \: cosine (cos \: A ) = \dfrac{AB}{AC}}$

$\sf{ \longrightarrow \: \dfrac{AB}{AC}}$

$\sf{ \longrightarrow \: \dfrac{4}{5} \: \: \: \: \bigstar}$

• tangent ( tan A )

$\sf{ \longrightarrow \: tangent (tan \: A) = \dfrac{BC}{AB}}$

$\sf{ \longrightarrow \: \dfrac{BC}{AB}}$

$\sf{ \longrightarrow \: \dfrac{3}{4} \: \: \: \: \bigstar}$

• cotangent ( cot A )

$\sf{ \longrightarrow \: cotangent (cot \: A) = \dfrac{AB}{BC}}$

$\sf{ \longrightarrow \: \dfrac{AB}{BC}}$

$\sf{ \longrightarrow \: \dfrac{4}{3} \: \: \: \: \bigstar}$

• secant ( sec A )

$\sf{ \longrightarrow \: secant (sec \: A) = \dfrac{AC}{AB}}$

$\sf{ \longrightarrow \: \dfrac{AC}{AB}}$

$\sf{ \longrightarrow \: \dfrac{5}{4} \: \: \: \: \bigstar}$

• cosecant ( cosec A )

$\sf{ \longrightarrow \: cosecant (cosec \: A ) = \dfrac{AC}{BC}}$

$\sf{ \longrightarrow \: \dfrac{AC}{BC}}$

$\sf{ \longrightarrow \: \dfrac{5}{3} \: \: \: \: \bigstar}$