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Solve the equation If the problem involved θ only, we would expect 2 solutions; one in the first quadrant and one in the second quadrant.But here our problem involves `2θ`, so we have to double the domain (θ values) to account for all possible solutions.
STEP 3: Check for angle multiples and remove them using the appropriate formulas.
STEP 4: Expand any equations you can, combine like terms, and simplify the equations.
As you gain more practice, you can skip or combine these steps when you recognize other identities.
STEP 1: Convert all sec, csc, cot, and tan to sin and cos.
We proceed as follows: We solve We can see from the graph that our 4 values are reasonable, since these are the only 4 values that satisfy `sin 2θ = 0.8`.
Note: We can always check our solutions with calculator, but it is easy to "miss out" on some of the required values if we only use calculator.You may wish to go back and have a look at Trigonometric Functions of Any Angle, where we see the background to the following solutions. Where the graph cuts the x-axis, that's where you'll find your solutions (the x-values that "work").Graphs also help you to understand why sometimes there is one answer, and sometimes many answers.The same ratio of sides happens at 150°, 390°, 510°, etc.Not only that, you can rotate backward (clockwise), and get negative angles. Because of this, most trig problems include a domain limitation (upper and lower limits for possible inputs).A trigonometric equation is an equation that involves trigonometric functions, ratios of the sides of a right triangle.Trig functions help us solve many kinds of problems.STEP 5: Replace cos powers greater than 2 with sin powers using the Pythagorean identities.STEP 6: Factor numerators and denominators, then cancel any common factors.The basic trig functions (or identities) are ratios of two of the three sides of a right triangle, and each function has a reciprocal function (where the numerator and denominator are reversed): When you're solving trig equations, you're looking for x (or some other value), using trig identities and the rules of algebra.You simplify the equation down to a single identity, such sin(x) = .5, then use your calculator or a table to find out the value of angle x.