Question

Sin 225° = sin (180° + 45°) =

Answer 1

Объяснение:

sin225=sin(180+45)= -sin45= -√2/2

Answer 2

sin 225° is equal to sin (180° + 45°).

First, we need to determine the reference angle for 45°. The reference angle is the positive acute angle formed between the terminal side of the given angle (45°) and the x-axis.

In this case, the terminal side of 45° is in the second quadrant (where sine is positive) and forms a right triangle with the x-axis. The reference angle is the acute angle formed between the x-axis and the hypotenuse of this right triangle.

We can see that the reference angle for 45° is 180° - 45° = 135°.

Since sin is positive in the second quadrant, we can now write sin 225° as sin (180° + 45°) = sin 135°.

Using the reference angle, we can determine the sin value in terms of the reference angle. In this case, sin 135° = sin (180° - 45°) = sin 45°.

The sine of 45° is a well-known value from the unit circle and is equal to 1/√2 or (√2)/2.

Therefore, sin 225° = sin (180° + 45°) = sin 135° = sin 45° = 1/√2 or (√2)/2.