Question

If sinθ=7/13 and cosθ=12/13 find tan θ and cot θ

Use Pythagorean Identities to find sin θ and tan θ if cos θ =-24/25 if the terminal side of θ lies in the third quadrant.

Answer 1

hellooo help me please

Answer 2

recall that for the point (x,y)
sinθ = y/r
cosθ = x/r
tanθ = y/x
So, for your two problems,
If sinθ=7/13 and cosθ=12/13 find tan θ and cot θ
Unfortunately, no angle θ has sinθ=7/13 and cosθ=12/13 since 7^2+12^2 ≠ 13^2
However, 5^2+12^2 = 13^2, so if
sinθ=5/13 and cosθ=12/13
then tanθ = sinθ/cosθ = 5/12

cos θ =-24/25 in QIII, so
x = -24
y = -7
r = 25
So,
sinθ = y/r = -7/25
tanθ = y/x = 7/24