What is the value of 3/4 (sin((15pi)/2))+2 ?

The value of 3/4 (sin((15pi)/2))+2 is 5/4

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3/4 (sin((15pi)/2))+2

\frac{3}{4} (sin (\frac{15 π}{2})) + 2

\frac{5}{4}

Solution steps

\frac{3}{4} (sin (\frac{15 π}{2})) + 2

= \frac{3}{4} sin (\frac{15 π}{2}) + 2

\frac{3}{4} sin (\frac{15 π}{2}) + 2 = \frac{3 sin ( \frac{15 π}{2} ) + 8}{4}

= \frac{3 sin ( \frac{15 π}{2} ) + 8}{4}

sin (\frac{15 π}{2}) = sin (\frac{3 π}{2})

= \frac{3 sin ( \frac{3 π}{2} ) + 8}{4}

Rewrite using trig identities:

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

= \frac{3 \cdot 2 sin ( \frac{3 π}{4} ) cos ( \frac{3 π}{4} ) + 8}{4}

Simplify

= \frac{6 sin ( \frac{3 π}{4} ) cos ( \frac{3 π}{4} ) + 8}{4}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{6 \cdot \frac{2}{2} ( - \frac{2}{2} ) + 8}{4}

Simplify

\frac{6 \cdot \frac{2}{2} ( - \frac{2}{2} ) + 8}{4} : \frac{5}{4}

= \frac{5}{4}

20 sin (15 0^{\circ})

lo g_{10} (sin (45.20249 9^{\circ}))

sin (8 0^{\circ}) sin (5) + cos (8 0^{\circ}) cos (5)

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

tan (4 1^{\circ}) \cdot 3

What is the value of 3/4 (sin((15pi)/2))+2 ?
The value of 3/4 (sin((15pi)/2))+2 is 5/4