Use the given information to find (a) sin(s+t), (b) tan(s+t), and (c) the quadrant of s+t. cos s = - 12/13 and sin t = 4/5, s and t in quadrant ll.

Part a)    

Part b)

Part c) (s+t) lie on Quadrant IV

Step-by-step explanation:

[Part a) Find sin(s+t)

we know that

step 1

Find sin(s)

we have

substitute

---> is positive because s lie on II Quadrant

step 2

Find cos(t)

we have

substitute

is negative because t lie on II Quadrant

step 3

Find sin(s+t)

we have

substitute the values

Part b) Find tan(s+t)

we know that

tex]tan(s + t) = (tan(s) + tan(t))/(1 - tan(s)tan(t))[/tex]

we have

step 1

Find tan(s)

substitute

step 2

Find tan(t)

substitute

step 3

Find tan(s+t)

substitute the values

Part c) Quadrant of s+t

we know that

 ----> (s+t) could be in III or IV quadrant

----> (s+t) could be in III or IV quadrant

Find the value of cos(s+t)

we have

substitute

we have that

-----> (s+t) could be in I or IV quadrant

 ----> (s+t) could be in III or IV quadrant

----> (s+t) could be in III or IV quadrant

therefore

(s+t) lie on Quadrant IV

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.