What is the value of 3cos(3.4pi) ?

The value of 3cos(3.4pi) is 3cos((7pi)/5)

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3cos(3.4pi)

3 cos (3.4 π)

3 cos (\frac{7 π}{5})

Decimal Notation

- 0.92705 \dots

Solution steps

3 cos (3.4 π)

= 3 cos (\frac{17}{5} π)

Rewrite as

= cos (2 \cdot \frac{17 π}{10})

Rewrite using trig identities:

cos (2 \cdot \frac{17 π}{10}) = 1 - 2 sin^{2} (\frac{17 π}{10})

cos (2 \cdot \frac{17 π}{10})

Use the Double Angle identity:

cos (2 x) = 1 - 2 sin^{2} (x)

= 1 - 2 sin^{2} (\frac{17 π}{10})

= 3 cos (\frac{17}{5} π)

Simplify:

\frac{17}{5} π = \frac{17 π}{5}

\frac{17}{5} π

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{17 π}{5}

= 3 cos (\frac{17 π}{5})

cos (\frac{17 π}{5}) = cos (\frac{7 π}{5})

cos (\frac{17 π}{5})

Rewrite

\frac{17 π}{5}

2 π + \frac{7 π}{5}

= cos (2 π + \frac{7 π}{5})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + \frac{7 π}{5}) = cos (\frac{7 π}{5})

= cos (\frac{7 π}{5})

= 3 cos (\frac{7 π}{5})

sin (10 3^{\circ})

cos (80. 4^{\circ})

37 sin (1 5^{\circ})

sin^{2} (1.5)

cos (2) + 1