Question

find all trigonometric ratios if sin theta =3/7​

Answer 1

Hi dear asker.

_______________

There are total of six trigonometric

functions:-

• Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent

_______________

According to question :-

sin(theta) = 3/7

Perpendicular / hypotenuse = 3/7 { sin(theta) = per. / hyp.) }

thus, perpendicular = 3 and Hypotenuse = 7

Using Pythagoras theorem for the other side:-

we know :-

(base)² + (perpendicular) ² = (hypotenuse)²

(base)² = (hypotenuse)² - (perpendicular)²

putting the respective values in above equation:-

(base)² = 7² - 3²

(base) ² = 49 - 9

(base)² = 40

base = √40.

________________________

Now :-

perpendicular = 3

hypotenuse = 7

base = √40.

____________________

sin(theta) = 3/7 (given)

cos(theta) = base/ hypotenuse

➡ √40/7

tan(theta) = perpendicular/base

➡ 7/3

cosec(theta)

➡1/sin(theta)

➡ 7/3

Sec(theta)

➡ 1/ cos(theta)

➡ 7/√40

cot(theta)

➡ 1/tan (theta)

➡ 3/7

__________________

Random thought :-

Intelligent people Fail.

but Hardworker Never Does.

__________________

thank you.

Answer 2

hope this helps u

$\huge{\mathcal{\pink{A}\green{N}\red{S}\blue{W} {E}\green{R}}}$

sin Ф= $\frac{3}{7}$ = $\frac{opp}{hyp}$

hyp²= opp²+adj²

adj²= 7²-3²

     = 49-9

adj = $\sqrt{40}$

cos Ф = $\frac{adj}{hyp}$

cos Ф =  $\frac{√40}{7}$

tan Ф =  $\frac{opp}{adj}$

tan Ф =  $\frac{3}{√40}$

we know that

cosec Ф = $\frac{1}{sinФ}$

cosec Ф  =   $\frac{7}{3}$

secФ = $\frac{1}{cos Ф}$

secФ=    $\frac{7}{√40}$

cot Ф = $\frac{1}{ tanФ}$

cot Ф =  $\frac{√40}{3}$