Question

Suppose that is an angle in standard position whose terminal side Intersects the unit circle at11 606161Find the exact values of sin 8, sec8, and tan.

Answer 1

`\begin{gathered} \sin \theta\text{ = }(60)/(61) \\ \sec \theta\text{ = -}(61)/(11) \\ \tan \theta\text{ = -}(60)/(11) \end{gathered}`

Step-by-step explanation

Step 1: The given coordinates placed the angle in the 4th quadrant.

`(x,\text{ y) = (-}(11)/(61),(60)/(61)\text{)}`

Step 2:

Note: Radius (r) for unit circle is 1.

`\sin \text{ }\theta\text{ = }(y)/(r)\text{ = }((60)/(61))/(1)\text{ = }(60)/(61)`
`\sec \text{ }\theta\text{ = }\frac{1}{\text{cos}\theta}\text{ = }(1)/((x)/(r))\text{ = }(r)/(x)\text{ = }(1)/((-11)/(61))\text{ = -}(61)/(11)`
`\tan \text{ }\theta\text{ = }(y)/(x)\text{ = }((60)/(61))/(-(11)/(61))\text{ = }(60)/(61)*-(61)/(11)\text{ = -}(60)/(11)`