An angle θ drawn in standard position terminates in the fourth quadrant. If sinθ= -2/5 then what is the value of cosθ?

Science & Mathematics by Anonymous 2018-05-13 23:07:12

Social Science

6 answers

Anonymous

sin(t) = opp/hyp = -2/5 adj = sqrt( 5^2 - 2^2) = sqrt(25-4) = sqrt(21) cos(t) = adj/hyp = sqrt(21)/5 Cos(t) is positive in quadrant IV (while sine is negative) https://gyazo.com/9a684de8a5eea07179bd27...
Anonymous

given that sinθ= -2/5 we know that sin²x + cos²x = 1 (-2/5) ²+ cos²x = 1 cos²x = 1 – 2/25 cos²x = 23/25 cosx = √23/5
Anonymous

Ans:
Anonymous

reference triangle for Θ is { √21 , - 2 , 5 }
Anonymous

Cosine is positive in the 4th Quadrant. cos(Θ) = √(1-sin²Θ) = √(1-4/25) = √21/5 ≈ 0.91652
Anonymous

rule (sinθ)^2+(cosθ)^2=1