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2 years ago

(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.

Mathematics

1 answer:

aliya0001 [1]2 years ago

5 0

Answer:

A = 2
B = 3

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

sin(π/4) = cos(π/4) = (√2)/2

cos(π/3) = 1/2

sin(π/3) = (√3)/2

So, the desired value is ...

sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

A = 2

B = 3

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