a-point-p11616061pleft-frac1161frac6061right-is-plotted-on-the-unit-circle-for-a

Question

A point ﻿P(−1161,6061)P\left(-\frac{11}{61},\frac{60}{61}ight)P(−6111​,6160​)﻿ is plotted on the unit circle for a certain angle ﻿θ	hetaθ﻿. Determine the values of the trigonometric functions ﻿sin⁡θ\sin	hetasinθ﻿, ﻿cos⁡θ\cos	hetacosθ﻿, ﻿tan⁡θ	an	hetatanθ﻿, ﻿cot⁡θ\cot	hetacotθ﻿, ﻿sec⁡θ\sec	hetasecθ﻿, and ﻿csc⁡θ\csc	hetacscθ﻿ corresponding to this point.

Accepted Answer

﻿sin⁡θ=6061\sin	heta=\frac{60}{61}sinθ=6160​﻿, ﻿cos⁡θ=−1161\cos	heta=-\frac{11}{61}cosθ=−6111​﻿, ﻿tan⁡θ=−6011	an	heta=-\frac{60}{11}tanθ=−1160​﻿, ﻿cot⁡θ=−1160\cot	heta=-\frac{11}{60}cotθ=−6011​﻿, ﻿sec⁡θ=−6111\sec	heta=-\frac{61}{11}secθ=−1161​﻿, ﻿csc⁡θ=6160\csc	heta=\frac{61}{60}cscθ=6061​﻿

Answer

﻿sin⁡θ=−1161\sin	heta=-\frac{11}{61}sinθ=−6111​﻿, ﻿cos⁡θ=6061\cos	heta=\frac{60}{61}cosθ=6160​﻿, ﻿tan⁡θ=−6011	an	heta=-\frac{60}{11}tanθ=−1160​﻿, ﻿cot⁡θ=−1160\cot	heta=-\frac{11}{60}cotθ=−6011​﻿, ﻿sec⁡θ=−6111\sec	heta=-\frac{61}{11}secθ=−1161​﻿, ﻿csc⁡θ=6160\csc	heta=\frac{61}{60}cscθ=6061​﻿

Answer

﻿sin⁡θ=6061\sin	heta=\frac{60}{61}sinθ=6160​﻿, ﻿cos⁡θ=−1161\cos	heta=-\frac{11}{61}cosθ=−6111​﻿, ﻿tan⁡θ=−6011	an	heta=-\frac{60}{11}tanθ=−1160​﻿, ﻿cot⁡θ=−1160\cot	heta=-\frac{11}{60}cotθ=−6011​﻿, ﻿sec⁡θ=6160\sec	heta=\frac{61}{60}secθ=6061​﻿, ﻿csc⁡θ=−6111\csc	heta=-\frac{61}{11}cscθ=−1161​﻿

Answer

﻿sin⁡θ=6061\sin	heta=\frac{60}{61}sinθ=6160​﻿, ﻿cos⁡θ=−1161\cos	heta=-\frac{11}{61}cosθ=−6111​﻿, ﻿tan⁡θ=−1160	an	heta=-\frac{11}{60}tanθ=−6011​﻿, ﻿cot⁡θ=−6011\cot	heta=-\frac{60}{11}cotθ=−1160​﻿, ﻿sec⁡θ=−6111\sec	heta=-\frac{61}{11}secθ=−1161​﻿, ﻿csc⁡θ=6160\csc	heta=\frac{61}{60}cscθ=6061​﻿