If tan theta equals 10/7 and if cos theta is less than 0 then whats sec theta, cos theta and sin theta

Question

Need help fast !!

Answer 1

tangent is opposite side over adjacent side

tanA = o/a = 10/7

hypotenuse is sqr(10^2 + 7^2)=sqr149)

sinA=opposite over hypotenuse = 10/sqr149

cosA=adjacent over hypotenuse = 7/sqr149

secA=1/cosA = 1/(7/sar149)=(sqr149)/7

but cosA<0, putting the angle A in quadrant III

so put negative signs in front of the above values for sine, cosine and secant of A

sinA=-10/sqr149

cosA = -7/sqr149

secA = -(sqr149)/7

square root of 149 is slightly more than 12, since 12 squared = 144

sqr149= about 12.2

sinA = -10/12.2 = -5/6.1=-0.82

cosA = -7/12.2=-0.57

secA =-12.2/7=-1.74

I'm not sure if it's politically correct anymore, but one way people

remember sine, cosine and tangent is an "Indian" name "SOHCAHTOA"

SOH for sine is opposite over hypotenuse

CAH for cosine is adjacent over hypotenuse

TOA for tangent is opposite over adjacent