Solve Trig Problems

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.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.

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.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.

The following identities are essential to all your work with trig functions. Quotient Identities: tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) Reciprocal Identities: csc(x) = 1/sin(x) sec(x) = 1/cos(x) cot(x) = 1/tan(x) sin(x) = 1/csc(x) cos(x) = 1/sec(x) tan(x) = 1/cot(x) Pythagorean Identities: sin The following seven step process will work every time.

It is rather tedious, and can take more time than necessary.

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.

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.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 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.For example, domains might be limited to 0° to 180°, 0° to 360°, -180° to 180°, etc.As a side note, remember that some trig problems work in radians instead of degrees. Radians use the π properties of a circle, and instead of expressing angles as part of a 360° circle, they express angles as a part of a 2π circle.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.

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