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 sin2x + cos2x + tan2x = 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. 586• 13, 17, 33, 39, 42, 45