7.4.2 – Solving Trig Equations, Cont’d

Sometimes, we may have more than one trig function at play while trying to solve Like having two variables

>1 trig function When we have more than one trig function, we want to try and simplify the equation in terms of a single trig function How? – Use identities – Expand or factor using algebra – Write in terms of sine and cosine, combine – Look for any like terms to cancel

Example. Solve the equation sin 2 x + cos 2 x + tan 2 x = 0.

Example. Solve the equation cosx – 1 = sinx – Hint: treat the left side as a binomial.

Verifying Solutions Similar to algebra, we must be able to verify that solutions of particular equations are accurate Options: – 1) Plug in, pull values from table – 2) Use calculator, be careful of typing answers in

Example. Verify for the equation that x = 2π/3 is a solution to 2 cosx + 1 = 0.

Using your calculator Sometimes, finding exact solutions may not be feasible In this event, we will jump to using our calculators, and treating them as an algebraic expression

To use your calculator: – 1) Write the function with all terms on a single side – 2) Plug in into your “graph” section – 3) Select an appropriate range – 4) Use the “find-zero” feature we have used before

Example. Estimate the solutions to the equation x tan(x) – 3 = 0 on the interval [0, 2π)

Example. Estimate the solutions to the equation 2 sin x = 1 – 2 cos x on the interval [0, 2π)

Assignment Pg , 17, 33, 39, 42, 45