What is the value of sin(600)+sec(660)-cot(690) ?

The value of sin(600)+sec(660)-cot(690) is -(sqrt(3))/2+2+sqrt(3)

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sin(600)+sec(660)-cot(690)

sin (60 0^{\circ}) + sec (66 0^{\circ}) - cot (69 0^{\circ})

- \frac{3}{2} + 2 + 3

Solution steps

sin (60 0^{\circ}) + sec (66 0^{\circ}) - cot (69 0^{\circ})

sin (60 0^{\circ}) = sin (24 0^{\circ})

= sin (24 0^{\circ}) + sec (66 0^{\circ}) - cot (69 0^{\circ})

sec (66 0^{\circ}) = sec (30 0^{\circ})

= sin (24 0^{\circ}) + sec (30 0^{\circ}) - cot (69 0^{\circ})

cot (69 0^{\circ}) = cot (15 0^{\circ})

= sin (24 0^{\circ}) + sec (30 0^{\circ}) - cot (15 0^{\circ})

Rewrite using trig identities:

sin (24 0^{\circ}) = 2 sin (12 0^{\circ}) cos (12 0^{\circ})

= 2 sin (12 0^{\circ}) cos (12 0^{\circ}) + sec (30 0^{\circ}) - cot (15 0^{\circ})

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Rewrite using trig identities:

sec (30 0^{\circ}) = 2

Use the following trivial identity:

cot (15 0^{\circ}) = - 3

= 2 \cdot \frac{3}{2} (- \frac{1}{2}) + 2 - (- 3)

Simplify

2 \cdot \frac{3}{2} (- \frac{1}{2}) + 2 - (- 3) : - \frac{3}{2} + 2 + 3

= - \frac{3}{2} + 2 + 3

csc (- \frac{7 π}{2})

arctan (\frac{50}{40})

arctan (\frac{6 3}{- 6})

(- 7) \cdot 0.15 \cdot 6.6 \cdot 1 0^{6} \cdot cos (6 5^{\circ})

sin (3 0^{\circ} + 18 0^{\circ})

What is the value of sin(600)+sec(660)-cot(690) ?
The value of sin(600)+sec(660)-cot(690) is -(sqrt(3))/2+2+sqrt(3)