Question

How do you solve \[\cos x = - 0.7\] between 0 and 2pi?

Answer 1

Hint: The given trigonometric question needed to be solved by finding the value of the variable “x”, for that we need to get the value of the numerical value in terms of “cos” function, here the value is in the range of zero and one which shows that the given function had a solution or we can say real solution, to find the number of solution we can solve further.

Formulae Used: \[ - \cos \theta = \cos (180 - \theta )\]

Complete step-by-step solution:
Here we know that the given question needs the value for the given function between zero and two pi, so for that we need to solve the question between these ranges.
Here we know that:
\[ \Rightarrow \cos x = - 0.7 = - \cos (45.57)\]
Now to remove the negative sign we have to use the property:
\[ \Rightarrow - \cos \theta = \cos (180 - \theta )\]
Using the above property in our question we get:
\[ \Rightarrow - \cos (45.57) = \cos (180 - 45.57) = \cos 134.43\]
This is one real solution for the question, now for more solution we can add the obtained angle with this angle, on solving we get:
\[ \Rightarrow 134.34 + 45.57 = 225.57\]
This is the second solution for the question within the range of angles given in the question, no further solutions are possible within the range of question now. So we obtained two possible angles for our expression.

Therefore the solution for the given question is 225.57.

Note: This question is also possible by making the graph of the given function, and after plotting the graph we have to draw a straight line parallel to x-axis, and perpendicular to y-axis, the cross section points between straight line and the curve is our required answer between the given range of question