Thread: Trigonometric and Hyperbolic identities

Question is as follows:-

Hence solve for t for values in the range 0 ≤ t ≤ 2 π rad:
5.5 Cos t + 7.8 Sin t = 4.5

Any help would be greatful, thanks

Originally Posted by boza100

Question is as follows:-

Hence solve for t for values in the range 0 ≤ t ≤ 2 π rad:
5.5 Cos t + 7.8 Sin t = 4.5

Any help would be greatful, thanks

Well it's a bit ugly but one approach would be to recall that and plug that in...


Isolate the radical and square it. This will give you a quadratic in sin(t) which you can solve using the quadratic formula. Check for extra, but not valid, solutions.

Also since in reality you should also work through the negative solution as well. And again check your solutions with the original equation.

-Dan

Another approach would be to use a linear combination identity to write the equation as:





Now, after finding the quadrant IV solution, use the identity to get the quadrant III solution.