Question

If sin a is 3 by 4 find cos a

Answer 1

Answer:

Explanation:

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Answer 2

Given:

$\sin(a) = \dfrac{3}{4}$

To find :

$\cos(a)$

Formula used :

$\implies \: sin( \theta) = \dfrac{p}{h}$

$\implies\cos( \theta) = \dfrac{b}{h}$

$\implies \: b = \sqrt{ {h}^{2} - {p}^{2} }$

where :

• p = perpendicular
• b = base
• h = hypotenuse

Solution :

$\implies \: sin( \theta) = \dfrac{p}{h}$

$\implies \sin(a) = \dfrac{3}{4}$

Therefore , p = 3 and h = 4

Now we will find b so that we can find out the value of Cos(a).

$\implies \: b = \sqrt{ {h}^{2} - {p}^{2} }$

put :-

• p = 3
• h = 4

$\implies \: b = \sqrt{ {4}^{2} - {3}^{2} }$

$\implies \: b = \sqrt{16 - 9 }$

$\implies \: b = \sqrt{7 }$

Now we will find value of cos(a) :-

$\implies\cos( \theta) = \dfrac{b}{h}$

$\implies\cos( a) = \dfrac{ \sqrt{7} }{4}$

Answer :

$\cos( a) = \dfrac{ \sqrt{7} }{4}$

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Learn more:-

1. Cosθ = base / hypotenuse

2. cossecθ = 1/ sinθ

3. sec θ = 1/cosθ

4. Cotθ = 1/ tanθ

5. Sin²θ+ Cos²θ= 1

6. Sec²θ - tan²θ = 1

7. cosec ²θ - cot²θ = 1

8. sin(90°−θ) = cos θ

9. cos(90°−θ) = sin θ

10. tan(90°−θ) = cot θ

11. cot(90°−θ) = tan θ

12. sec(90°−θ) = cosec θ

13. cosec(90°−θ) = sec θ

14. Sin2θ = 2 sinθ cosθ

15. cos2θ = Cos²θ- Sin²θ

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