If 3sin tita - cos tita=0,how do I find the value of 3tan tita=1(0° less than or equal to tita less than or equal to 360°) with the use of a graph book?
3sin tita - cos tita=0
3sin Ø = cos Ø , ..... theta , not tita
divide both sides by cos Ø
3 sinØ/cosØ = 1
3 tanØ = 1
tanØ = 1/3
By "the use of a graph book", I will assume that you mean the
table of trig values one could find in most math text books in past years.
Since 1/3 = appr .3333, go to the tangent column, find the value closest
to .3333 and note the angle. You should get 18° as the nearest degree.
From your CAST rule, you also know that the tangent trig ratio is positive in quadrants I and III,
so Ø = 18° or Ø = 198°
Ø or φ = phi
Θ or θ = theta
Ø is fast access on my Mac (Option-shift-O), that's why I use it for an angle.
To find the value of 3tan(theta) = 1 given the equation 3sin(theta) - cos(theta) = 0 and using a graph book, you can follow these steps:
Step 1: Plot the graph of the equation 3sin(theta) - cos(theta) = 0.
- In a graph book, draw the axes (x-axis and y-axis).
- Mark the theta values on the x-axis and the corresponding values of the equation on the y-axis.
- Sketch the curve that represents the equation by connecting the points obtained.
- The curve will intersect the x-axis at different points.
Step 2: Find the values of theta where the curve intersects the x-axis.
- Identify the x-coordinates where the curve intersects the x-axis.
- These x-values correspond to the values of theta where 3sin(theta) - cos(theta) = 0.
Step 3: Evaluate 3tan(theta) at the values of theta obtained.
- For each value of theta where 3sin(theta) - cos(theta) = 0, substitute that value into the equation 3tan(theta) = 1.
- Calculate the value of 3tan(theta) for each theta, and see if it equals 1.
Step 4: Analyze the results.
- If you find any values of theta where 3tan(theta) = 1, note down those values.
- If there are no such values, it means that there is no solution to the equation 3tan(theta) = 1 based on the given equation 3sin(theta) - cos(theta) = 0.
By following these steps and using your graph book, you can determine whether or not there are any values of theta for which 3tan(theta) equals 1, based on the given equation 3sin(theta) - cos(theta) = 0.