How do you find the exact values of the six trigonometric function of theta if the terminal side of theta in the standard position contains the point (2,1)?

1 Answer
Shell
Nov 6, 2016

Draw a right triangle in the first quadrant using the x axis as one of the legs. Find the hypotenuse r using the Pythagorean theorem, and then use the values of x, y, and r to find the six trig functions.

Explanation:

![http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U19_L1_T3_text_final.html](useruploads.socratic.org)

For the point (2,1), x=2 and y=1 in the diagram above.

Using the Pythagorean theorem, find r.

x^2 +y^2 = r^2

2^2 +1^2 =r^2

5=r^2

r=sqrt5

To find the 6 trig functions use x=2, y=1, r=sqrt5

sintheta=y/r = 1/sqrt5 = sqrt5/5

csctheta = 1/sintheta =sqrt5/1 =sqrt5

costheta=x/r =2/sqrt5 = (2sqrt5)/5

sectheta = 1/costheta = sqrt5/2

tantheta=y/x=1/2

cottheta=1/tantheta=2/1= 2

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