What is the value of -sin(pi/3)+sec^2(pi/3) ?

The value of -sin(pi/3)+sec^2(pi/3) is -(sqrt(3))/2+4

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-sin(pi/3)+sec^2(pi/3)

- sin (\frac{π}{3}) + sec^{2} (\frac{π}{3})

- \frac{3}{2} + 4

Decimal Notation

3.13397 \dots

Solution steps

- sin (\frac{π}{3}) + sec^{2} (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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}

= \frac{3}{2}

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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

Simplify

= - \frac{3}{2} + 4

sec (\frac{- π}{4})

4 cos (4 0^{\circ})

sin (90 0^{\circ})

100 sin (4 5^{\circ})

1 - sin (\frac{π}{6})

What is the value of -sin(pi/3)+sec^2(pi/3) ?
The value of -sin(pi/3)+sec^2(pi/3) is -(sqrt(3))/2+4