Trigonometric Functions

Question

P(2,–6) is a point on the terminal side of theta in standard position. Identify the exact value of the six trigonometric functions for theta.

Answer 1

sin θ = y/r, cos θ = x/r, tan θ = y/x

csc θ, sec θ and cot θ are the reciprocals

r=sqrt((2)^2+(-6)^2)=sqrt(40)

y=-6 , x=2 and r=sqrt(40)

sin θ = y/r=-6/sqrt(40)= (-3sqrt(10))/10

cos θ = x/r= 2/sqrt(40)=sqrt(10)/10

tan θ = y/x=-6/2=-3



You do csc θ, sec θ and cot θ

Answer 2

(2,-6) is in the 4th quadrant

it forms a right triangle with hypotenuse = sqr(36+4) =sqr40 =2sqr10

sinA = -6/2sqr10 = -3/sqr10

cscA = -sqr10/3

cosA =2/2sqr10 = 1/sqr10

secA = sqr10

tanA = -6/2 =-3

cotA = -1/3

sinA=y/h = 1/cscA

cosA=x/h =1/secA

tanA =y/x = 1/cotA

cscA =h/y

secA=h/x

cotA =x/y