If sin A = 3/5, find the values of cos A and tan A

Question

Q) If sin A = ${\frac{3}{5}$, find the values of cos A and tan A

Sapling Academy · Accepted Answer

[Approach: We can calculate the value of cos A by trigonometric identity of sin2 A + cos2 A = 1, and then calculate tan A = sin A / cos A]

Step 1: Since we know that sin2 A + cos2 A = 1

given that sin A = =${\frac{3}{5}$

∴ $(\frac{3}{5})^2$ + cos2 A = 1

∴ $(\frac{9}{25})$ + cos2 A = 1

∴ cos2 A = 1 - $(\frac{9}{25})$ = $(\frac{25 - 9}{25})$ = $\frac{16}{25}$

∴ cos A = $\sqrt{\frac{16}{25}}$ = ${\frac{4}{5}$

Step 2: Let's calculate value of tan A : = $\frac{\sin A}{\cos A}$ = $\frac{\frac{3}{5}}{\frac{4}{5}}$

=$\frac{3}{5}$ x $\frac{5}{4}$   =   $\frac{3}{\cancel 5}$ x $\frac{\cancel 5}{4}$   =   $\frac{3}{4}$

Therefore, the values of cos A is ${\frac{3}{5}$ and tan A is ${\frac{3}{4}$.

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