Question

By using identity
If cot Φ=8/15 ,then find the value of sin Φand sec Φ​

Answer 1

Answer:

Sin THETHA=opposite/hypotenuse

therefore,sin THETHA=15/17

sec THETHA=hypotenuse/adjacent

therefore, sec THETHA=17/8

Answer 2

Answer:

cot A = 8/15 …….(1)

And we know,

cot A = 1/tan A

Also by definition,

Cot A = Base side adjacent to ∠A/ Perpendicular side opposite to ∠A …. (2)

On comparing equation (1) and (2), we get;

Base side adjacent to ∠A = 8

Perpendicular side opposite to ∠A = 15

So, by using Pythagoras theorem to △ABC, we have

$\rm \: AC^2 = AB^2 +BC^2$

Substituting values for sides from the figure

$\rm \: AC^2 = 82 + 152$

$\rm \: AC^2 = 64 + 225$

$\rm \: AC^2 = 289$

$\rm \: AC = √289$

$\rm \: AC = 17$

Therefore, hypotenuse =17

By definition,

sin A = Perpendicular/Hypotenuse

⇒ sin A= BC/AC

sin A= 15/17 (using values from the above)

Also,

sec A= 1/ cos A

⇒ secA = Hypotenuse/ Base side adjacent to ∠A

∴ sec A= 17/8