Question

Find cos (st) given that cos s

OA
O G.
O D.
10
3-4√5
10
3-4√6
10
-3-4√/5
10
withs in quadrant ill, and cost-
3
with t in quadrant III.

Answer 1

Answer:To find cos(st) given that cos(s) = -3/10 and cos(t) = -3, we can use the trigonometric identity for the cosine of a product of two angles:

cos(st) = cos(s) * cos(t) - sin(s) * sin(t)

First, let's determine sin(s) using the Pythagorean identity:

sin(s) = √(1 - cos^2(s))

= √(1 - (-3/10)^2)

= √(1 - 9/100)

= √(91/100)

= √91/10

Next, let's determine sin(t) using the Pythagorean identity:

sin(t) = √(1 - cos^2(t))

= √(1 - (-3)^2)

= √(1 - 9)

= √(-8)

= √8 * i

= 2√2 * i

Now we can substitute these values into the cosine of the product formula:

cos(st) = cos(s) * cos(t) - sin(s) * sin(t)

= (-3/10) * (-3) - (√91/10) * (2√2 * i)

= 9/10 - 2√2/10 * √91 * i

= 9/10 - (2√2√91)/10 * i

= 9/10 - (√182/10) * i

Therefore, cos(st) is approximately 9/10 - (√182/10) * i.