If cos ⁡θ=−8/17, and 180°θ<270°, what is sin θ?

-15/17

Step-by-step explanation:

One method is to use Pythagorean identity.

sin² θ + cos² θ = 1

sin² θ + (-8/17)² = 1

sin² θ + 64/289 = 1

sin² θ = 225/289

sin θ = ±15/17

Since θ is in the third quadrant, sin θ < 0.  So sin θ= -15/17.

Another method is to draw a triangle in the third quadrant, with angle θ, adjacent side -8, and hypotenuse 17.  Use Pythagorean theorem to find the opposite side:

c² = a² + b²

17² = (-8)² + b²

b = -15

Therefore, sin θ = -15/17

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.