What is the value of 2-4cos((3pi)/2) ?

The value of 2-4cos((3pi)/2) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2-4cos((3pi)/2)

2 - 4 cos (\frac{3 π}{2})

2

Solution steps

2 - 4 cos (\frac{3 π}{2})

Rewrite using trig identities:

cos (\frac{3 π}{2}) = cos^{2} (\frac{3 π}{4}) - sin^{2} (\frac{3 π}{4})

= 2 - 4 (cos^{2} (\frac{3 π}{4}) - sin^{2} (\frac{3 π}{4}))

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= 2 - 4 (- \frac{2}{2})^{2} - (\frac{2}{2})^{2}

Simplify

2 - 4 (- \frac{2}{2})^{2} - (\frac{2}{2})^{2} : 2

= 2

ln tan (\frac{π}{3}) + sec (π^{3})

arctan (tan (\frac{83}{63} π))

tan (\frac{18}{2 45})

arctan (0.1875)

tan (\frac{6}{5})