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Sine, Cosine, Tangent Ratios

Video Tutorial- How to write sohcahtoa ratios, given side lengths

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What do we mean by 'ratio' of sides?

 Sine, cosine and tangent of an angle represent the ratios that are always true for given angles. Remember these ratios only apply to right triangles. The 3 triangles pictured on the left illustrate this. Although the side lengths of the right triangles are different, each one has a 37° angle, and as you can see, the sine of 37 is always the same! In other words, sin(37) is always .6 ! (Note: I rounded to the nearest tenth) That's, of course, why we can use a calculator to find these sine, cosine and tangent ratios.
Practice Problems

problemIn the triangle on the left, what side is adjacent to $$\angle MLN$$ ?

problem Calculate $$cos(\angle MLN)$$
 Cosine

problem Calculate $$cos(\angle MNL)$$
 Cosine

problem What is the sine ratio of $$\angle ACB$$ in the triangle on the right?

problem Which angle on the left has a tangent of $$\frac{3}{4}$$ ?
Challenge Problem
Be careful!
In the triangle on the left, which angle has a sine ratio of 2.6?
problemIn $$\triangle JKL$$, sin(k) = $$\frac{3}{5}$$, what is tan(k)?
problem In $$\triangle ABC , cos(b) = \frac{7}{25}$$, what is sin(b)?