SOLUTION: Find the exact value of the given expression. tan(1/2 cos^-1(2/3))

Question 866238: Find the exact value of the given expression.
tan(1/2 cos^-1(2/3))
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of the given expression.
tan(1/2 cos^-1(2/3))
let x=angle whose cos=2/3
cosx=2/3
sinx=√(1-cos^2x)=√(1-4/9)=√(5/9)=√5/3
tan(1/2 cos^-1(2/3))=tan(x/2)
Identity: tan(x/2)=sinx/(1+cosx)=(√5/3)/(1+(2/3))=(√5/3)/(5/3)=√5/5
calculator check:
cosx=2/3
x≈48.19˚
x/2≈24.09
tan(x/2)≈tan(24.09)≈0.4471�
exact value as calculated=√5/5≈0.4471�
RELATED QUESTIONS
Find the exact value of the expression. sin(cos^-1 2/3 - tan^-1... (answered by KMST)

how do you find the exact value of the expression cos(sin^-1 1/3 - tan^-1... (answered by lwsshak3)

Find the exact value of the expression tan[cos^-1 (1/2)]: (answered by stanbon)

Write the given expression in terms of x and y only. sin(tan^−1(x) −... (answered by ikleyn)

Find the exact value of... (answered by jsmallt9)

1-Find the exact value of this expression. sin^-1(-1/2) 2-Find the exact value of this (answered by stanbon)

Find the exact value of the expression sin((tan^-1 3/4) +(cos^-1... (answered by lwsshak3)

find the exact value of cos(sin inverse 1/3 - tan inverse... (answered by lwsshak3)

Find the exact value of the given expression. cos ^-1... (answered by stanbon)