Question

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

Answer 1

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