Question

Please help algebra question number one. Thx 1) If cos = -5/13 and tan <0 what is exact value of sin 0?5/12-12/1312/13-5/12

Answer 1

The quadrant for which cos Θ is negative is at Quadrant II and III.

The quadrant for which tan Θ is negative is at Quadrant II and IV.

The angle must be therefore found, in Quadrant II. Drawing a diagram of the angle, we have the following

Solve first for the missing side using the Pythagorean Theorem

`\begin{gathered} a^2+b^2=c^2 \\ a^2+(-5)^2=(13)^2 \\ a^2+25=169 \\ a^2=169-25 \\ a^2=144 \\ √(a^2)=√(144) \\ a=12 \end{gathered}`

The missing side is 12, therefore,

`\sin\theta=(12)/(13)`