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Question

A point ﻿P(1237,−3537)P\left(\frac{12}{37},-\frac{35}{37}ight)P(3712​,−3735​)﻿ 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=−3537\sin	heta=-\frac{35}{37}sinθ=−3735​﻿, ﻿cos⁡θ=1237\cos	heta=\frac{12}{37}cosθ=3712​﻿, ﻿tan⁡θ=−3512	an	heta=-\frac{35}{12}tanθ=−1235​﻿, ﻿cot⁡θ=−1235\cot	heta=-\frac{12}{35}cotθ=−3512​﻿, ﻿sec⁡θ=3712\sec	heta=\frac{37}{12}secθ=1237​﻿, ﻿csc⁡θ=−3735\csc	heta=-\frac{37}{35}cscθ=−3537​﻿

Answer

﻿sin⁡θ=−3537\sin	heta=-\frac{35}{37}sinθ=−3735​﻿, ﻿cos⁡θ=1237\cos	heta=\frac{12}{37}cosθ=3712​﻿, ﻿tan⁡θ=−1235	an	heta=-\frac{12}{35}tanθ=−3512​﻿, ﻿cot⁡θ=−3512\cot	heta=-\frac{35}{12}cotθ=−1235​﻿, ﻿sec⁡θ=3712\sec	heta=\frac{37}{12}secθ=1237​﻿, ﻿csc⁡θ=−3735\csc	heta=-\frac{37}{35}cscθ=−3537​﻿

Answer

﻿sin⁡θ=1237\sin	heta=\frac{12}{37}sinθ=3712​﻿, ﻿cos⁡θ=−3537\cos	heta=-\frac{35}{37}cosθ=−3735​﻿, ﻿tan⁡θ=−3512	an	heta=-\frac{35}{12}tanθ=−1235​﻿, ﻿cot⁡θ=−1235\cot	heta=-\frac{12}{35}cotθ=−3512​﻿, ﻿sec⁡θ=3712\sec	heta=\frac{37}{12}secθ=1237​﻿, ﻿csc⁡θ=−3735\csc	heta=-\frac{37}{35}cscθ=−3537​﻿

Answer

﻿sin⁡θ=3537\sin	heta=\frac{35}{37}sinθ=3735​﻿, ﻿cos⁡θ=−1237\cos	heta=-\frac{12}{37}cosθ=−3712​﻿, ﻿tan⁡θ=−3512	an	heta=-\frac{35}{12}tanθ=−1235​﻿, ﻿cot⁡θ=−1235\cot	heta=-\frac{12}{35}cotθ=−3512​﻿, ﻿sec⁡θ=−3712\sec	heta=-\frac{37}{12}secθ=−1237​﻿, ﻿csc⁡θ=3735\csc	heta=\frac{37}{35}cscθ=3537​﻿