Question

1. Given that cosθ≈0.646 where θ is in quadrant IV, find the values of sinθ and tanθ to the nearest thousandth

a. sinθ=−0.763; tanθ=−1.181

b. sinθ=−0.763; tanθ=−0.847

c. sinθ=0.763; tanθ=0.847

d. sinθ=0.763; tanθ=1.181


2. Terran’s running rate is 4 miles per hour faster than her walking rate. She can run 21 miles in the same amount of time it takes her to walk 9 miles. What are her walking and running rates in miles per hour? Write and solve a rational equation to answer the question. Let x be Terran’s walking rate

a. 21/x+4=9/x; Terran walks at 2 miles per hour and runs at 6 miles per hour.

b. 21/x=9/x−4; Terran walks at 7 miles per hour and runs at 10 miles per hour.

c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.

d. 21/x+4=9/x; Terran walks at 3 miles per hour and runs at 7 miles per hour.

Answer 1

d.) sinθ=0.763; tanθ=1.181

c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.

Explanation:

Given that:

θ is in the IV quadrant (All is positive) that is sin, cos and tan are all positive.

Cosθ = 0.646

Θ = Cos^-1(0.646)

θ = 49.75930

Hence,

Tanθ = tan(49.75930) = 1.1816365 = 1.182

Sinθ = sin(49.75930) = 0.7633373 = 0.763

2.)

Let

Walking rate = x mph

Running rate = x + 4 mph

21 miles run time = 9 miles walk time

Recall :

Time = distance / speed or rate

21 / (x + 4) = 9 / x

Cross multiply :

21 * x = 9(x + 4)

21x = 9x + 36

21x - 9x = 36

12x = 36

x = 36 /12

x = 4 mph = walking rate

Running rate = x + 4 = 4 + 4 = 8 mph