Question

if cos theta = 5/13 then find the value of cos theta, tan theta , cot theta ,sec theta and cosec theta ..

Answer 1

EXPLANATION.

Cos ø = 5/13 = B/H = Base/Hypotenuse.

By using the Pythagorean theorem,

we get,

→ H² = P² + B²

→ (13)² = P² + (5)²

→ 169 = P² + 25

→ 169 - 25 = P²

→ 144 = P²

→ P = √144

→ P = 12

→ Sin ø = P/H = Perpendicular/Hypotenuse

Sin ø = 12/13.

→ Cos ø = B/H = Base/Hypotenuse = 5/13.

→ Tan ø = P/B = Perpendicular/Base = 12/5.

→ Csc ø = H/P = Hypotenuse/Perpendicular

Csc ø = 13/12.

→ Sec ø = H/B = Hypotenuse/Base = 13/5.

→ Cot ø = B/P = Base/Perpendicular = 5/12.

Answer 2

Answer:

GIVEN : Cos A = 5/13

Since, Cos A = base / hypotenuse

By Pythagoras Theoerem

h²=p²+b²

=> 13² = p² + 5²

=> 169 = p² + 25

=> 169-25 = p²

=> 144 = p²

$= > \sqrt{144 = p}$

=> 12 = p

Therefore

p= 12 , b = 5 , h = 13

Cos A = 5/13

Tan A = p/b

= 12/5

cot A = b/p

= 5/12

sec A = h/b

= 13/5

cosec A = h/p

= 13/12

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