Question

Algebra 2: PLEASE HELP ME!!

Answer 1

Looks more like Trig than Algebra II

They want us to apply the sum angle formula to
`\sin(x + (5 \pi)/(6))`

5π/6 is 150°; I find it easier to think in degrees.

When the tangent of x is 3/4 that's a right triangle with opposite 3, adjacent 4 so hypotenuse 5. So a sine of 3/5 and a cosine of 4/5, both positive because we're told x is in the first quadrant.

The sine sum angle formula is

`\sin(a+b) = \sin a \cos b + \cos a \sin b`

`\sin(x+(5\pi)/(6)) = \sin x \cos (5\pi)/(6) + \cos x \sin (5\pi)/(6)`

We know sin 150° = sin 30° = 1/2 and cos 150° = - cos 30° = -√3/2

`\sin(x+(5\pi)/(6)) = \frac 3 5 (- √(3)/2) + \frac 4 5 (1/2)`

`\sin(x+(5\pi)/(6)) = ( 4- 3√(3))/(10)`

Third choice