Solve Trig Problems

Solve Trig Problems-88
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.

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The following is a simple example: 30° is just one of the solutions.

An angle is a measure of rotation, and if you keep rotating you'll get more angles with the same sine.

I use Scientific Notebook or similar math software to graph the functions for me.

You can use this Online Graphing Calculator to solve the following equations (or check your solutions) .

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.STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity.(x) = 1 STEP 7: Since this is one of the Pythagorean identities, we know it is true, and the problem is done.The 7 step method works both sides and meets in the middle, like a V.The trick to solve trig identities is intuition, which can only be gained through experience.The more basic formulas you have memorized, the faster you will be.If you've been working in trigonometry, you've probably seen sines, cosines, tangents, and angle relationships until it's nearly driven you nuts.Before you lock yourself in a psych ward somewhere, let's take a look at some of them, and see if we can't make them just a bit easier.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.


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