Question

Please help ASAP! The terminal side of an angle θ in standard position passes through the point (2,-5). calculate the values of the six trigonometric functions for angle θ.

Answer 1

`sin(x)=(opp)/(hyp)=(5)/(√(21))=(5√(21))/(21)\\cos(x)=(adj)/(hyp)=(2)/(√(21))=(2√(21))/(21)\\tan(x)=(opp)/(adj)=(5)/(2)\\csc(x)=(hyp)/(opp)=(√(21))/(5)\\sec(x)=(hyp)/(adj)=(√(21))/(2)\\cot(x)=(adj)/(opp)=(2)/(5)`

Explanation:

Start by drawing out the triangle on the graph:

(See picture)

(By the drawing you can judge me that I am a really bad artist)

Theta and the side lengths are labeled, the hypotenuse has a length of √21 by Pythagora's theorem. Now, time to put everything to the trigonometric functions:

`sin(x)=(opp)/(hyp)=(5)/(√(21))=(5√(21))/(21)\\cos(x)=(adj)/(hyp)=(2)/(√(21))=(2√(21))/(21)\\tan(x)=(opp)/(adj)=(5)/(2)\\csc(x)=(hyp)/(opp)=(√(21))/(5)\\sec(x)=(hyp)/(adj)=(√(21))/(2)\\cot(x)=(adj)/(opp)=(2)/(5)`

(Suppose that x is theta as I can't type it)

By some basic understanding that's all that I can do.