What is the value of 59-25cos^2(0)-50sin(0) ?

The value of 59-25cos^2(0)-50sin(0) is 34

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59-25cos^2(0)-50sin(0)

59 - 25 cos^{2} (0) - 50 sin (0)

34

Solution steps

59 - 25 cos^{2} (0) - 50 sin (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 59 - 25 \cdot 1^{2} - 50 \cdot 0

Simplify

= 34

arctan (\frac{2.2907}{1.6326})

sin (- 1 \frac{1}{2})

cos (6 0^{\circ}) 6

cos^{2} (1 0^{\circ}) - sin^{2} (1 0^{\circ})

- 3 sin (\frac{7 π}{4})

What is the value of 59-25cos^2(0)-50sin(0) ?
The value of 59-25cos^2(0)-50sin(0) is 34