Evaluate the expression under the given conditions. cos(θ − ϕ); cos θ = 3 5 , θ in quadrant iv, tan ϕ = − 15 , ϕ in quadrant ii

1 answer:

7 0

Begin with cos(θ) = 5/13, θ in Quadrant IV

you should distinguish the 5-12-13 right-angled triangle

and then cosØ = adjacent/hypotenuse

x = 5, r = 13 , y = -12, since Ø is in IV

and sinØ = -12/13

also tan(ϕ) = −√15 = -√15/1 = y/x and ϕ is in II,

y = √15 , x = -1

r^2 = x^2 + y^2 = 15+1 = 16

r = 4

sinϕ = √15/4 , cosϕ = -1/4
you must know that:

cos(θ − ϕ) = cosθcosϕ + sinθsinϕ

= (5/13)(-1/4) + (-12/13)(√15/4)

= -5/52 - 12√15/52

= (-5-12√15)/52

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