Find sin θ if cot θ = - 4 and cos θ < 0.
a) - 17
b) sqrt 17 / 17
c)-1/4
d) sqrt 17 / 4

The correct option is B

Step-by-step explanation:

The correct option is B.

Solution:

We have given that

cot θ = - 4

cos θ < 0

This shows that both the ratios are negative. So they lie in second quadrant because both are negative.

cot θ = - 4  it means that tan θ = -1/4 which shows that two sides opposite = 1 and adjacent = -4

Now we could find hypotenuse by Pythagorean theorem:

Hypotenuse = √(1)²+(-4)² = √1+16

=√17

Sin θ  = perpendicular(opposite)/hypotenuse

Sin θ =1/√17

Now multiply and divide by √17

Sin θ=  1/√17*√17/√17

Sin θ = √17/17

Thus the correct option is B

Yes, it's proportional because each orange costs $1.50 and this stays true throughout the whole list. If you continue the count, it will mean that $12 should get you 8 oranges. I found this by dividing the cost of 2 by 2 to find the cost of one at that level, and checked, using multiplication, to see if every other amount continued with the same price, and it did. I found that 12 dollars is 8 oranges by dividing 12 by 1.5.