What is the value of cos(-(17pi)/3) ?

The value of cos(-(17pi)/3) is 1/2

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cos(-(17pi)/3)

cos (- \frac{17 π}{3})

\frac{1}{2}

Solution steps

cos (- \frac{17 π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{17 π}{3}) = cos (\frac{17 π}{3})

= cos (\frac{17 π}{3})

cos (\frac{17 π}{3}) = cos (\frac{5 π}{3})

= cos (\frac{5 π}{3})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= (- 1) (- \frac{1}{2}) - 0 \cdot \frac{3}{2}

Simplify

= \frac{1}{2}

cos (\frac{7 π}{5})

tan (arcsin (\frac{7}{8}))

cos (37. 5^{\circ}) cos (7.5)

\frac{tan ( 14 0 ^{\circ} ) - tan ( 6 0 ^{\circ} )}{1 + tan ( 14 0 ^{\circ} ) tan ( 6 0 ^{\circ} )}

(sec (\frac{π}{4}))^{2}