Sine, Cosine, Tangent Ratios

Practice writing the ratios

---

Related: sohcahtoa home | Introduction to Sine, Cosine, Tangent | Find Side Length using sin, cos, tan
Right Triangle Calculator | sohcahtoa worksheet

---

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

In the triangle on the left, what side is adjacent to MLN? Adjacent Side ML What side is the hypotenuse? Hypotenuse LN Calculate cos(MLN) Cosine cos(MLN)= adjacent/hypotenuse= 8/10 = .8 Calculate cos(MNL) Cosine cos(LMN) = adjacent/hypotenuse=6/10 = .6

What is the sine ratio in the triangle on the right? Answer Remember that the sine ratio is the side opposite the angle (c) / hypotenuse. Therefore sine(C) = 6/10 or .6

What is the cosine ratio in the triangle on the right? Answer Remember that the cosine ratio is the side adjacent to the angle (x) / hypotenuse. Therefore cos(c) = 4/5 or .8

What is the tangent ratio in the triangle on the right? Answer Remember that the tangent ratio is the side opposite /adjacent sides. Therefore tan(b) = 12/9 or 1.3

Find the sine, cosine and tangent of ? Answers sin(a)= opp/hyp = 12/13 = .923 cos(a)= adj/hyp = 9/13 = .69 tan(a)= opp/adj = 12/9 = 1.3

What is sin(1)? Answer sin(1)=opposite/hypotenuse = 24/25 = .96 What is cos(1)? Answer cos1 = adjacent/hypotenuse = 7/25 =.28

What is sin(2), cos(2) & tan(2)? Answer sin(2) =3/5= .6 cos(2) = 4/5 = .8 tan(2) = 3/4 = .75

---

Related: sohcahtoa home | Introduction to Sine, Cosine, Tangent | Find Side Length using sin, cos, tan
Sine Cosine Calculator | sohcahtoa worksheet

---