Answer: See step by step. Replace the x with theta
Step-by-step explanation: Since sin is less than zero, and secant is positive. This means the trig values are in Quadrant 4.
We know that secФ=17/15. We need to find sin,cos,tan,csc, and cot.
We can find tangent by using the identity
[tex]tan^{2} (x)+ 1=sec^{2} (x)[/tex] where x is theta.
[tex]tan^{2} (x)+1=\frac{289}{225}[/tex]
[tex]tan^{2} (x)+\frac{225}{225} =\frac{289}{225}[/tex]
[tex]tan^{2}(x)=\frac{64}{225}[/tex]
tan x=[tex]\frac{8}{15}[/tex], Tangent in the fourth quadrant is negative so the answer is instead
[tex]tan x= -\frac{8}{15}[/tex]
We can find cotangent by taking the recipocial of tan so
[tex]cot=-\frac{15}{8}[/tex]
We can find cos by taking reciprocal of sec remeber that cosine is positive in 4th quadrant so the answer is
[tex]cos =\frac{15}{17}[/tex]
We can find sin by doing quoteint identies.
[tex]\frac{sin x}{cos x} =tan x[/tex]
[tex]\frac{ sin x}{15/17} =-\frac{8}{15}[/tex]
[tex]sin x= -\frac{8}{17}[/tex]
To find csc, take reciprocal of sine.
[tex]csc=\frac{-17}{8}[/tex]
