SOLUTION: given that cos 2a =11/61 and 0 deg<2a<45 deg, determine the exact values of sin a, cos a, tan a, csc a, sec a, and cot a.

Question 1079025: given that cos 2a =11/61 and 0 deg<2a<45 deg, determine the exact values of sin a, cos a, tan a, csc a, sec a, and cot a.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Given: cos(2A) = 11/61
Using the trig identity cos(2A) = 1 - 2sin^2(A), we can solve for sin(A)
sin(A) = sqrt(50/122)
cos(2A) can also be written as cos(2A) = cos^2(A) - sin^2(A) -> 11/61 = cos^2(A) - 50/122
This gives cos(A) = sqrt(72/122)
tan(A) = sin(A)/cos(A) = sqrt(50/72)
I will leave it as an exercise to complete the rest.
RELATED QUESTIONS
given that cos 2a =1/3 and 0 deg<2a<90 deg, determine the exact values of sin a, cos a,... (answered by tommyt3rd)

given that cos2a =2/5 and 0<2a<90, determine the exact values of sin a, cos a, tan a, csc (answered by Edwin McCravy)

given cos(2a)=-17/18 and 0<2a (answered by solver91311)
Find the exact values of sin 2a, cos 2a, and tan 2a. tan a=2, pi < a <... (answered by lwsshak3)
Find the exact values of the trigonometric functions for sin, cos, tan, csc, sec, and cot (answered by stanbon)
find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, π < a <... (answered by lwsshak3)
A function value and a quadrant are given. Find the other five functions values. Give... (answered by lwsshak3)
a function value and a qudrant are given, find the other five function values. give... (answered by Edwin McCravy)
Assume that a is an angle in standard position whose terminal side contains the point... (answered by lwsshak3)