Question

Sin100⁰*cos440⁰+sin800⁰*cos460⁰​

Answer 1

Ответ:

$\sin \left(100^{\circ \:}\right)\cos \left(440^{\circ \:}\right)+\sin \left(800^{\circ \:}\right)\cos \left(460^{\circ \:}\right)\\=\sin \left(100^{\circ \:}\right)\cos \left(80^{\circ \:}\right)+\sin \left(80^{\circ \:}\right)\cos \left(100^{\circ \:}\right)\\=\sin \left(100^{\circ \:}+80^{\circ \:}\right)\\=\sin \left(180^{\circ \:}\right)=0$

Объяснение:

Answer 2

To calculate the value of the expression sin(100°) * cos(440°) + sin(800°) * cos(460°), you can use trigonometric identities and properties to simplify the expression.

First, let's deal with the angles that are outside the standard range of 0° to 360°:

1. Angle 440° is equivalent to 440° - 360° = 80°.
2. Angle 800° is equivalent to 800° - 2 * 360° = 80°.

So, the expression becomes:

sin(100°) * cos(80°) + sin(80°) * cos(80°).

Now, you can use the identity sin(2θ) = 2sin(θ)cos(θ) to simplify further:

sin(100°) * cos(80°) + sin(80°) * cos(80°) = 2sin(80°)cos(80°).

Next, you can use the identity sin(2θ) = sin(2(90° - θ)) = sin(180° - 2θ) to rewrite sin(80°) as sin(180° - 2 * 80°):

2sin(80°)cos(80°) = 2sin(180° - 2 * 80°)cos(80°).

Now, you can use the identity sin(180° - θ) = sin(θ) to simplify further:

2sin(180° - 2 * 80°)cos(80°) = 2sin(80°)cos(80°).

At this point, you can use the identity sin(2θ) = 2sin(θ)cos(θ) once more to simplify:

2sin(80°)cos(80°) = 2 * (1/2) * sin(160°) = sin(160°).

So, sin(100°) * cos(440°) + sin(800°) * cos(460°) simplifies to sin(160°).

Now, calculate the value of sin(160°):

sin(160°) = sin(180° - 20°) = sin(20°).

You can use a calculator to find the value of sin(20°). It's approximately equal to 0.3420.

So, the final result is approximately 0.3420.