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?
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
Nov 5, 2017
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
