What is the value of 7cos(90)+4sin(180+pi/3) ?

The value of 7cos(90)+4sin(180+pi/3) is 7cos(pi/2)+4sin((4pi)/3)

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7cos(90)+4sin(180+pi/3)

7 cos (9 0^{\circ}) + 4 sin (18 0^{\circ} + \frac{π}{3})

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

Decimal Notation

- 3.46410 \dots

Solution steps

7 cos (9 0^{\circ}) + 4 sin (18 0^{\circ} + 6 0^{\circ})

Rewrite as

= sin (2 \cdot 12 0^{\circ})

Rewrite using trig identities:

sin (2 \cdot 12 0^{\circ}) = 2 sin (12 0^{\circ}) cos (12 0^{\circ})

sin (2 \cdot 12 0^{\circ})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (12 0^{\circ}) cos (12 0^{\circ})

= 7 cos (9 0^{\circ}) + 4 sin (18 0^{\circ} + 6 0^{\circ})

Simplify

= 7 cos (9 0^{\circ}) + 4 sin (24 0^{\circ})

sin (0.002)

arcsin (csc (- \frac{5 π}{2}))

cos (\frac{π}{2} + 1)

30 cos (15 0^{\circ})

2 arcsec (2) + arcsin (\frac{1}{2})

What is the value of 7cos(90)+4sin(180+pi/3) ?
The value of 7cos(90)+4sin(180+pi/3) is 7cos(pi/2)+4sin((4pi)/3)