Answered

1.) Find tan θ, given that sin θ = -4/5 and cos θ > 0.

a.) -5/3

b.) -4/3

c.) 3/5

d.) 5/4

I got 4/3, but that's not an option.


2.) Suppose θ is an angle in standard position with cos θ > 0. In which quadrants could the terminal side of θ lie? Select two answers.

a.) I

b.) II

c.) III

d.) IV

Verified Answer :

1 the cosine  is > 0 is in the 4th quadrant if the sine is negative
the tan will be -4/3

1) The value of tan θ is given by; B: -4/3

2) The quadrants in which the terminal sides of θ could lie are;

a: I and d: IV

Trigonometric Ratios

We are given that sin θ = -4/5

The quadrants that sin is negative are quadrants III and IV.

Now, we know that sin is opposite/hypotenuse.

Thus;

Length of adjacent side from pythagoras theorem will be 3.

Now, we are told that cos θ > 0. This means that it is either in the first or fourth quadrant as that is where it is positive. Thus;

cos θ = 3/5

tan θ = sin θ/cos θ

tan θ = (-4/5)/(3/5)

tan θ = -4/3

2) We are told that cos θ > 0.

Since cos is only positive in quadrants I and IV, then those are the only two possible terminal sides

Read more about trigonometric ratios at; https://brainly.com/question/12172664

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