Question

Use the given function value, and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
sec θ = 5

cot(90° − θ)=

sin θ=

Answer 1

do you know what quadrant you are in?

Answer 2

does not provide that information

Answer 3

then you cannot really do the problem, but we can assume we are in quadrant 1 and make everything positive

Answer 4

first we find \(\cos(x)=\frac{1}{\sec(x)}=\frac{1}{5}\)

Answer 5

then by pythagoras we find \(\sin(x)\)

Answer 6

third side via \(\sqrt{5^2-1^2}=\sqrt{24}\) so \(\sin(x)=\frac{\sqrt{24}}{5}\)

Answer 7

co-function identity tells us \(\cot(90-x)=\tan(x)\) and since we have cosine and sine, we have tangent, that is \(\tan(x)=\frac{\sqrt{24}}{1}=\sqrt{24}\)