What is the value of 20sin(1/2 pi(1.7)-pi(2.2)) ?

The value of 20sin(1/2 pi(1.7)-pi(2.2)) is 10sqrt(\sqrt{(5-\sqrt{5))/2}+2}

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20sin(1/2 pi(1.7)-pi(2.2))

20 sin (\frac{1}{2} π (1.7) - π (2.2))

10 \frac{5 - 5}{2} + 2

Solution steps

20 sin (\frac{1}{2} π (1.7) - π (2.2))

= 20 sin (\frac{1}{2} π \frac{17}{10} - π \frac{11}{5})

Simplify:

\frac{1}{2} π \frac{17}{10} - π \frac{11}{5} = - \frac{27 π}{20}

= 20 sin (- \frac{27 π}{20})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{27 π}{20}) = - sin (\frac{27 π}{20})

= 20 (- sin (\frac{27 π}{20}))

Simplify

= - 20 sin (\frac{27 π}{20})

Rewrite using trig identities:

sin (\frac{27 π}{20}) = - \frac{1 - cos ( \frac{7 π}{10} )}{2}

= - 20 - \frac{1 - cos ( \frac{7 π}{10} )}{2}

- 20 - \frac{1 - cos ( \frac{7 π}{10} )}{2} = 102 - cos (\frac{7 π}{10}) + 1

= 102 - cos (\frac{7 π}{10}) + 1

Rewrite using trig identities:

cos (\frac{7 π}{10}) = - \frac{2 5 - 5}{4}

= 102 - (- \frac{2 5 - 5}{4}) + 1

Simplify

102 - (- \frac{2 5 - 5}{4}) + 1 : 10 \frac{5 - 5}{2} + 2

= 10 \frac{5 - 5}{2} + 2

- cos (4)

tan (0) - 0

sec (\frac{5 π}{8})

tan^{2} (3 0^{\circ}) + csc^{2} (6 0^{\circ})

10 \cdot csc (2 3^{\circ})

What is the value of 20sin(1/2 pi(1.7)-pi(2.2)) ?
The value of 20sin(1/2 pi(1.7)-pi(2.2)) is 10sqrt(\sqrt{(5-\sqrt{5))/2}+2}