The point #(7,24)# is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

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Answer 1 · 2017-09-22T21:35:38

See explanation.

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

#r=sqrt(x^2+y^2)#

Here it is: #r=sqrt(7^2+24^2)=sqrt(49+576)=sqrt(625)=25#

Now we can calculate all 6 trig, functions:

#sinalpha=y/r=24/25#

#cosalpha=x/r=7/25#

#tanalpha=y/x=24/7=1 3/7#

#cotalpha=x/y=7/24#

#secalpha=r/x=25/7=3 4/7#

#csc alpha=r/y=25/24= 1 1/24#