Suppose θ is an angle in the fourth quadrant with cosθ=x/4. Find expressions for the other five trig functions in terms of x?

Im not sure how to solve this problem? To start out do you sketch a triangle and try to figure out the missing side?

1 Answer
Jim G.
Nov 5, 2017

#"see explanation"#

Explanation:

#"using the trig. identity"#

#•color(white)(x)sin^2theta+cos^2theta=1#

#rArrsintheta=+-sqrt(1-cos^2theta)#

#"since "theta" is in the fourth quadrant then only the"#
#"cos and sec ratios are positive, all others are negative"#

#•color(white)(x)costheta=x/4#

#rArrsintheta=-sqrt(1-(x/4)^2)#

#color(white)(rArrsintheta)=-sqrt(1-x^2/16)#

#color(white)(rArrsintheta)=-sqrt((16-x^2)/16)=-1/4sqrt(16-x^2)#

#•color(white)(x)tantheta=sintheta/costheta-sqrt(16-x^2)/xto(x!=0)#

#•color(white)(x)cottheta=1/tantheta=-x/sqrt(16-x^2)#

#•color(white)(x)sectheta=1/costheta=4/x#

#•color(white)(x)csctheta=1/sintheta=-4/sqrt(16-x^2#

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