Solve the equation for cos theta-tan theta=0 for greater than or egual to zero but less than 2pi. Write your answer as a multiple of pi, if possible form the following choices:
pi , 5pi
A. --- ----
4___ 4
B. pi 3pi 5pi 7pi
----- '----- '-----'-----
4_____ 4_____ 4______4
C. pi 3pi 3pi 7pi
----- '----- '-----'-----
2_______4______2_____4
D. pi 7pi 3pi 11pi
----- '----- '-----'-----
2________6______2_____6
cos ( theta ) - tan ( theta) = 0
tan ( theta ) = sin (theta ) / cos( theta )
cos ( theta ) - tan ( theta ) =0
cos ( theta ) = tan ( theta )
cos ( theta ) = sin ( theta ) / cos ( theta )
cos^2 ( theta) = sin ( theta )
Now go on:
wolframalpha dot com
When page be open in rectangle type :
solve cos^2 ( theta) = sin ( theta )
and click =
After few seconds you will see solution.
Then click option Show steps
cosØ - tanØ = 0
cosØ - sinØ/cosØ = 0
multiply by cosØ
cos^2Ø - sinØ = 0
(1 - sin^2Ø) - sinØ = 0
sin^2Ø + sinØ - 1 = 0
sinØ = (-1 ± √5)/2
sinØ = .618034 or -1.608 , the last is not possible since sinØ has to be between -1 and +1
Ø = 38.17° from my calculator (or 141.83°)
All your choices are in radians in multiples of π/2, π/4 or π/6
which would be multiples of 90°, 45° or 30°
None of these match,
btw, my answers satisfies the original equation.
To solve the equation cos(theta) - tan(theta) = 0, we can use the fact that tan(theta) = sin(theta)/cos(theta).
Substituting this into the equation, we get cos(theta) - sin(theta)/cos(theta) = 0.
To simplify this equation, we can multiply through by cos(theta) to get cos^2(theta) - sin(theta) = 0.
Now, rearranging the equation, we have cos^2(theta) = sin(theta).
Using the Pythagorean identity, sin^2(theta) + cos^2(theta) = 1, we can substitute sin^2(theta) = 1 - cos^2(theta) into our equation:
1 - cos^2(theta) + cos^2(theta) = 0
Simplifying, we have 1 = 0, which is not possible.
Therefore, there are no solutions to the equation cos(theta) - tan(theta) = 0 in the given interval [0, 2pi].
None of the choices provided are correct.