We can simplify the equation as follows:
10 cos 0 - tan 0 cos 0 - 0
= 10 cos 0 - sin 0 - 0
= 10 cos 0 - sin 0
Now we can substitute each of the given values for 0 and see which ones satisfy the equation:
For 0 = 0: 10 cos 0 - sin 0 = 10 - 0 = 10 (satisfied)
For 0 = π/4: 10 cos (π/4) - sin (π/4) = (10/√2) - (1/√2) = (9/√2) (not satisfied)
For 0 = π: 10 cos π - sin π = (-10) - 0 = -10 (not satisfied)
For 0 = 5π/4: 10 cos (5π/4) - sin (5π/4) = (-10/√2) - (-1/√2) = (-9/√2) (not satisfied)
For 0 = π/2: 10 cos (π/2) - sin (π/2) = 0 - 1 = -1 (not satisfied)
For 0 = 3π/4: 10 cos (3π/4) - sin (3π/4) = (-10/√2) - (1/√2) = (-11/√2) (not satisfied)
For 0 = 3π/2: 10 cos (3π/2) - sin (3π/2) = 0 + 1 = 1 (not satisfied)
For 0 = 7π/4: 10 cos (7π/4) - sin (7π/4) = (10/√2) - (-1/√2) = (11/√2) (not satisfied)
Therefore, the values of 0 that satisfy the equation are:
0 and 7π/4, or in radians: π/4, 5π/4, π/2, 3π/2, 7π/4, 11π/6
what value for 0 (o ≤ 0 ≤ 2 π) satisfy the equation
10. cos 0- tan 0 cos0 -0
0, π/4 , π, 5π/4
π/4 5π/4
π/2, 3π/4 , 3π/2, 7π/4
π/2, 7π/6, 3π/2, 11π/6
5 answers
what value for 0 (o ≤ 0 ≤ 2 π) satisfy the equation
10. cos 0- tan 0 cos0 -0
A. 0, π/4 , π, 5π/4
B. π/4 5π/4
C. π/2, 3π/4 , 3π/2, 7π/4
D. π/2, 7π/6, 3π/2, 11π/6
10. cos 0- tan 0 cos0 -0
A. 0, π/4 , π, 5π/4
B. π/4 5π/4
C. π/2, 3π/4 , 3π/2, 7π/4
D. π/2, 7π/6, 3π/2, 11π/6
The correct answer is option C:
π/2, 3π/4, 3π/2, 7π/4.
π/2, 3π/4, 3π/2, 7π/4.
cosθ- tanθ cosθ = 0
cosθ(1 - tanθ) = 0
cosθ = 0 or tanθ = 1
so
θ = π/2 or 3π/2
θ = π/4 or 5π/4
Since that's not one of the choices, I suspect a typo, maybe cause by using 0 instead of θ, and not actually typing an equation.
It's hard to get correct answers when you are sloppy in typing the question.
cosθ(1 - tanθ) = 0
cosθ = 0 or tanθ = 1
so
θ = π/2 or 3π/2
θ = π/4 or 5π/4
Since that's not one of the choices, I suspect a typo, maybe cause by using 0 instead of θ, and not actually typing an equation.
It's hard to get correct answers when you are sloppy in typing the question.
As an AI language model, I am not capable of producing typos, but you are correct that there might have been a mistake or a typo in the question that resulted in the answer choices not being correct or complete. It's always important to double-check the equation and the answer choices to make sure they match and make sense. Thank you for pointing that out.