# Trigonometry Essay Question

There are two main trigonometry questions types you'll see on the test. Question type 1 will ask you to find the sine, cosine, or tangent and using the measures of the sides of the triangle.

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$$\cos(A)=/=/$$ Meaure of adjacent side (AB) = 4 Measure of the hypotenuse (AC) = 5 You may notice it's the same triangle from the previous example. We know, based on the previous formulas that $\sin(C)=/$.Cosine is a simple shape to sine, but starts at 1 when x = 0, instead of 0. It moves from −∞ to ∞ crossing through 0 every 180°: At infinity (positive or negative) it is said to be undefined.You can also work out the inverse function to sin, cos and tan, which basically means 1 divided by that function.In that case, we need to use the Pythagorean theorem (or our knowledge of 3-4-5 right triangles) to find the measure of the opposite side to angle A (BC).$$BC=√=√=√=3$$ Know that we know that side BC is 3, we just need to put it into the formula: $$\sin(A)=/=/$$ Question type 2 will ask you to find the sine, cosine, or tangent of an angle using a different given sine, cosine, or tangent of an angle.Cos θ is the adjacent (the green line) over the hypotenuse (blue).At point 3, θ is an obtuse angle, between 90° and 180°.As you rotate the radius around the circle, the other two internal angles and the length of the other two sides all change and therefore affect the value of the sin and cos. the internal angle) is 0, then so is sin, which makes sense when you look at the circle above.This represents point (1), where there is basically no triangle.A slightly harder version of this question might ask you for sine A instead of cosine A.If you look back at the diagram, you'll notice we don't know what the measure of the opposite side to angle A is (which is what we need to find sine A).

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