Question

if sin theta = 12/13 find tan theta cos theta cosec theta sec theta cot theta​

Answer 1

Answer:

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Given: sin θ = 12/13

To find: cos θ and tan θ

Solution: sin θ = 12/13

In a right-angled triangle, sin θ = 12/13

Perpendicular (P)/ Hypotenuse (H) = 12/13

⇒ Let P = 12k and H = 13k

By using Pythagoras Theorem, H² = P² + B²

(13k)² = (12k)² + B²

169k² = 144k² + B²

B² = 25k²

B = 5k

Now, cos θ =  Base/Hypotenuse

cos θ = 5k/13k

∴ cos θ = 5/13

tan θ = sin θ/cos θ

tan θ = 12/13 × 13/5

∴ tan θ = 12/5

∴ cos θ = 5/13 and tan θ = 12/5

Step-by-step explanation:

Answer 2

Step-by-step explanation:

given

$\sin( \theta) = \frac{12}{13}$

so

$\cos \theta = \sqrt{1 - { \sin}^{2} \theta } \\ \\ \cos \theta = \sqrt{1 - \frac{144}{169} } \\ \\ = \sqrt{ \frac{25}{169} } \\ \\ = \frac{5}{13}$

so

$\cosec \theta = \frac{13}{12} \\ and \: \\ \sec \theta = \frac{13}{5}$

And

$tan \theta = \frac{sin \theta}{cos \theta} \\ \\ = \frac{ \frac{12}{13} }{ \frac{5}{13} } \\ \\ = \frac{12}{5} \\ \\ so \: \: \: \: cot \theta = \frac{1}{tan \theta} \\ = \frac{5}{12}$