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