Question

If sin A = 3/4 , calculate cos A and tan A. Solution:​

Answer 1

Step-by-step explanation:

As per the provided information in the given question, we have :

• $\sf {\sin \: A = \dfrac{3}{4} }$

We've been asked to calculate the value of cos A and tan A.

Here,

$\twoheadrightarrow \sf{\quad { \sin \: A = \dfrac{3}{4}\dots {(1)}}}$

As, we know that,

$\twoheadrightarrow \sf{\quad { \sin \: \theta = \dfrac{P}{H} \dots {(2)} }}$

So, here we can say that :

$\twoheadrightarrow \sf{\quad { \dfrac{P}{H} = \dfrac{3}{4} }}$

Thus,

• Perpendicular (P) = 3
• Hypotenuse (H) = 4

• C A L C U L A T I N G ⠀B A S E :

By using Pythagoras property,

↠⠀⠀⠀H² = B² + P²

↠⠀⠀⠀(4)² = B² + (3)²

↠⠀⠀⠀16 = B² + 9

↠⠀⠀⠀16 – 9 = B²

↠⠀⠀⠀7 = B²

↠⠀⠀⠀√7 = B

Therefore, base is √7. Now,

$\twoheadrightarrow \quad \boxed{\sf{ \cos \: A = \dfrac{B}{H}}}$

Substitute the values.

$\twoheadrightarrow \sf{\quad { \cos \: A = \dfrac{\sqrt{7}}{4} }} \; \bigstar$

Similarly,

$\twoheadrightarrow \quad \boxed{\sf{ \tan \: A = \dfrac{P}{B}}}$

Substitute the values

$\twoheadrightarrow \sf{\quad { \tan \: A = \dfrac{3}{\sqrt{7}} }} \; \bigstar$

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Learn More :⠀⠀⠀⠀

$\bull \sf{\quad { \sin \: \theta = \dfrac{P}{H} }}$

$\bull \sf{\quad { \cosec \: \theta = \dfrac{H}{P} }}$

$\bull \sf{\quad { \cos \: \theta = \dfrac{B}{H} }}$

$\bull \sf{\quad { \sec \: \theta = \dfrac{H}{B} }}$

$\bull \sf{\quad { \tan \: \theta = \dfrac{P}{B} }}$

$\bull \sf{\quad { \cot \: \theta = \dfrac{B}{P} }}$

Answer 2

Answer:

cos A = (√7)/4

tan A = 3/(√7).

Explanation:

We know, sin² A + cos² A = 1

=> cos A = √(1 - sin² A) = √(1 - 9/16) = √(7/16) = (√7)/4.

Now, tan A = sin A / cos A

=> tan A = 3/4 × 4/(√7) = 3/(√7).