What is sin(arctan(y/4)) ?

The solution to sin(arctan(y/4)) is (ysqrt(16+y^2))/(16+y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sin(arctan(y/4))

simplify

sin (arctan (\frac{y}{4}))

\frac{y 16 + y ^{2}}{16 + y ^{2}}

Solution steps

sin (arctan (\frac{y}{4}))

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{y}{4} ) 1 + ( \frac{y}{4} ) ^{2}}{1 + ( \frac{y}{4} ) ^{2}}

Simplify

= \frac{y 16 + y ^{2}}{16 + y ^{2}}

cos (x - \frac{π}{3}) 1

9 + 9 tan^{2} (x)

sin (x) sin (- x)

tan (θ) + tan (\frac{π}{2} - θ)

sin (\frac{3 π}{2} + θ)

What is sin(arctan(y/4)) ?
The solution to sin(arctan(y/4)) is (ysqrt(16+y^2))/(16+y^2)