The exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24
The function is given as:
cos(x) = 24/25, tan(x) < 0
The sine function is calculated using:
sin^2(x) + cos^2(x) = 1
So, we have:
sin^2(x) + (24/25)^2 = 1
Collect like terms
sin^2(x) = -(24/25)^2 + 1
Evaluate the squares
sin^2(x) = -576/625 + 1
Take the LCM
sin^2(x) = (625-576)/625
Evaluate
sin^2(x) = 49/625
Take the square roots
sin(x) = -7/25 --- sin(x) is negative because tan(x) < 0
The tangent function is calculated using:
tan(x) = sin(x)/cos(x)
This gives
tan(x) = (-7/25) / (24/25)
Evaluate
tan(x)= -7/24
Hence, the exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24
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Complete question
Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)
cos(x) = 24/25, tan(x)< 0
sin(x) =
tan(x) =
