Question

Use the cosine of a sum and cosine of a difference identities to find cos(s+t) and cos(s - D). 3 cos s= - 5 and sint= s and t in quadrant III cos ( st) cos (S-1)= ว 2 5 6/6-4 5 6/6-4 25 6/6+4 5 66+4 25 ab -4 5

Answer 1

Remember that

cos(s+t)=cos(s)cos(t)-sin(s)sin(t)

and

cos(s-t)=cos(s)cos(t)+sin(s)sin(t)

In this problem we have

cos(s)=-3/5

sin(t)=-1/5

s and t in quadrant III

that means

cos(s) and cos(t) are negative

sin(s) and sin(t) are negative

step 1

Find sin(s)

Apply

cos^2(s)+sin^2(s)=1

substitute

(-3/5)^2+sin^2(s)=1

sin^2(s)=1-9/25

sin^2(s)=16/25

sin(s)=-4/5

step 2

Find cos(t)

cos^2(t)+sin^2(t)=1

cos^2(t) +(-1/5)^2=1

cos^2(t)=1-1/25

cos^2(t)=24/25

cos(t)=-2√6/5

step 3

Find

cos(s+t)=cos(s)cos(t)-sin(s)sin(t)

substitute given values

cos(s+t)=(-3/5)(-2√6/5)-(-4/5)(-1/5)

cos(s+t)=(6√6/25)-(4/25)

cos(s+t)=(6√6-4)/25

step 4

Find cos(s-t)

cos(s-t)=cos(s)cos(t)+sin(s)sin(t)

cos(s-t)=(-3/5)(-2√6/5)+(-4/5)(-1/5)

cos(s-t)=(6√6/25)+(4/25)

cos(s-t)=(6√6+4)/25