Question

(sin 30 + cis 60°)× sin 135​

Answer 1

(Sin 30 градусов + cos 60градусов) * sin 135 градусов=
(1/2 +1/2)*корень из 2/2 = 1* корень из 2/2= корень из 2/2

Answer 2

To evaluate the expression, let's break it down step by step:

1. sin 30: The sine of 30 degrees is equal to 0.5.
2. cis 60°: The cis function represents the complex number in trigonometric form. For an angle of 60 degrees, cis 60° is equal to cos 60° + i sin 60°. The cosine of 60 degrees is 0.5, and the sine of 60 degrees is √3/2. Therefore, cis 60° can be written as 0.5 + i(√3/2).
3. (sin 30 + cis 60°): Adding sin 30 and cis 60° gives 0.5 + 0.5 + i(√3/2) = 1 + i(√3/2).
4. sin 135: The sine of 135 degrees is -√2/2.

Finally, we multiply (1 + i(√3/2)) by -√2/2:

(1 + i(√3/2)) × (-√2/2) = -√2/2 - (√6/4)i

Therefore, (sin 30 + cis 60°) × sin 135 is equal to -√2/2 - (√6/4)i.