Question

Sin(-π:4)•cos(-π:3)•tg(-π:6)​

Answer 1

Ответcos( – π/6) × sin( – π/3) + tg( – π/4) =

=cos( π/6) × (–sin( π / 3)) – tg(π/4)=

=(√3/2) ×(–√3/2)–1=(3/4)–1=–1/4.:

Объяснение:

cos( – π/6) × sin( – π/3) + tg( – π/4) =

=cos( π/6) × (–sin( π / 3)) – tg(π/4)=

=(√3/2) ×(–√3/2)–1=(3/4)–1=–1/4.

Answer 2

To calculate the value of the expression sin(-π/4) * cos(-π/3) * tan(-π/6), you can follow these steps:

1. Calculate sin(-π/4): sin(-π/4) = -sin(π/4) because the sine function is an odd function. sin(π/4) = 1/√2 because sin(π/4) is the sine of 45 degrees, which is 1/√2 in radians.

   Therefore, sin(-π/4) = -(1/√2).

2. Calculate cos(-π/3): cos(-π/3) = cos(π/3) because the cosine function is an even function. cos(π/3) = 1/2 because cos(π/3) is the cosine of 60 degrees, which is 1/2 in radians.

3. Calculate tan(-π/6): tan(-π/6) = -tan(π/6) because the tangent function is an odd function. tan(π/6) = 1/√3 because tan(π/6) is the tangent of 30 degrees, which is 1/√3 in radians.

   Therefore, tan(-π/6) = -(1/√3).

Now, multiply these values together: (-1/√2) * (1/2) * (-(1/√3)) = -((1/√2) * (1/2) * (1/√3))

To simplify further, you can multiply the constants together: -((1/√2) * (1/2) * (1/√3)) = -((1/√(223)))

Now, simplify the denominator: -((1/√(223))) = -((1/√(12)))

Finally, simplify the square root: -((1/√(12))) = -((1/(2√3)))

So, the value of the expression sin(-π/4) * cos(-π/3) * tan(-π/6) is -1/(2√3).