2. Solving Trigonometric Equations Using Inverses
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sinθ | cosθ | cosθsinθ | tanθ | |
---|---|---|---|---|
θ=30∘ | 21 | 23 | 2321 | 33 |
θ=45∘ | 22 | 22 | 2222 | 1 |
θ=60∘ | 23 | 21 | 2123 | 3 |
θ=90∘ | 1 | 0 | 01 | Undefined |
The tangent of an angle that measures 60∘ is 3. Let's now construct a 30∘-60∘-90∘ triangle. Since we will also need to use the unit circle, our right triangle will have a hypotenuse that measures 1.
In this type of special triangle, the length of the shorter leg is half the length of the hypotenuse, and the length of the longer leg is 3 times the length of the shorter leg.
Next, let's locate this triangle in the coordinate plane. Since the given value is negative, our solutions will be located in the quadrants that have negative tangent values — Quadrant II and Quadrant IV.
We can draw a 30∘-60∘-90∘ triangle on a unit circle with the measurements found above in these quadrants. We will place the 60∘ angle at the origin.