Question

Q6 Q17.) Use the given information to find the exact value of each of the following.

Answer 1

The angle is in the III quadrant so both x and y are negative.

Given x=-5,

y=-sqrt(13^2 - (-5)^2)

=-sqrt(169-25)

=-sqrt(144)

=-12

cos(theta)=-12/13

tan(theta)=-12/-5=12/5

sin(2theta)=2sin(theta)cos(theta)=120/169

cos(2theta)=1 - 2(sin(theta))^2=119/169

tan2θ=2tan(theta)/(1-(tan(theta)^2)=120/119

Answer 2

sinθ = -5/13 and θ lies in Q III
recognizing 5 n 13 are part of Pythagorean triple: 5, 12, 13
cosθ = -12/13
tanθ = 5/12

sin2θ = 2sinθcosθ = 2*(-5/13)*(-12/13) = 120/169

cos2θ = 1 - 2(sinθ)^2 = 1 - 2(-5/13)^2 = 1 - 50/169 = 119/169

tan2θ = sin2θ / cos2θ = 120/119 = 1 1/119