Question

2. If Cos 0 =
15
17
then find sin 0​

Answer 1

Correct Question:

If cos θ = 15/17 , then find sin θ

Solution:

Using,

sin² θ + cos² θ = 1

Simplifying

sin θ = √1 - cos² θ

Now , substituting the value of cosθ

→  sin θ = √1 - (15/17)²

→  sin θ = √1 - 225/289

→  sin θ = √[(289 - 225)/289]

→ sin θ = √[64/289]

→  sin θ = √64/√289

→  sin θ = 8/17

Hence , sin θ = 8/17

★ Knowledge enhancer  :-

Trigonometric identities

→  1st identity  : sin² A + cos²A = 1

→  2nd identity : sec²A - tan²A = 1

→  3rd identity : cosec²A - cot²A = 1

Answer 2

${ \bold { \underline{\large{Correct \: Question : - }}}} \:$

If Cos θ = $\sf\dfrac{15}{17}$ then find sin θ

${ \bold { \underline{\large{ Required\: Answer : - }}}} \:$

${ \bold { \underline{\large{Given : - }}}} \:$

Cos θ = $\sf\dfrac{15}{17}$

${ \bold { \underline{\large{ To \: Find : - }}}} \:$

sin θ = ?

${ \bold { \underline{\large{Solution : - }}}} \:$

As we know that

sin² θ + cos² θ = 1

Now ,simplifying

sin θ = √1 - cos² θ = 1

Now,substituting the value of cos

sin θ = $\sqrt{1 } - \sf\dfrac{ {15}^{2} }{17}$

sin θ = √1 - $\sf\dfrac{225}{289}$

sin θ = $\sf\dfrac{ \sqrt{1 - 225} }{289}$

sin θ = $\sqrt{ \sf\dfrac{64}{289} }$

sin θ. = $\sf\dfrac{ \sqrt{64} }{ \sqrt{289}}$

sin θ = $\sf\dfrac{8}{17}$

Hence,

sin θ = $\sf\dfrac{8}{17}$