If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ?

2 square root of 2 over 3
negative 2 square root of 2 over 3
2 square root of 2
negative 2 square root of 2

2√2 / 3 (first answer choice)

Step-by-step explanation:

If tan Ф < 0, then Ф must be in either Quadrant II or Quadrant IV.

If sin Ф = +1/3, then Ф (for this problem) is in Quadrant II.

Remembering that sin Ф = opp / hyp = 1 / 3, we use the Pythagorean Theorem to find the adj side:

adj² + 1² = 3²,  or

adj² + 1 = 9, or    adj² = 8.  Since Ф is in Quadrant II, adj is negative.

The value of cos Ф = adj / hyp = √8 / 3 = 2√2 / 3

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5