How do we use trig ratios? Trigonometric Ratios How do we use trig ratios? M2 Unit 2: Day 3

In a Triangle, we know that the angles have a sum of 180 and that the two acute angles are complementary So, if one angle is Then the other one is

Assume X Z Y

Trigonometric Ratios: Are ratios of the lengths of 2 sides of a right triangle. There are 3 basic trig ratios: sine, cosine, and tangent (abbreviated sin, cos, and tan) The value of a trig ratio depends only on the measure of the acute angle, not on the particular triangle being used to compute the value.

SOHCAHTOA If you can remember his name, then you can remember your trig ratios!

Opposite means “across from the angle” Adjacent means “attached to the angle” Hypotenuse is always opposite the right angle.

Label the hypotenuse, opposite and adjacent for angle A.

Label the hypotenuse, opposite and adjacent for angle .

Label the hypotenuse, opposite and adjacent for angle X. Z Y Now, label the hypotenuse, opposite and adjacent for angle y.

Now find the sine, the cosine, and the tangent of . Notice something about the sine and cosine ratios? How about the tangent ratios?

Now find the sine, the cosine, and the tangent of . 2 13 5 12 Now find the sine, the cosine, and the tangent of . Notice something about the sine and cosine ratios? How about the tangent ratios?

Find tan . Round to four decimal places. 42 40 B A 58 Tan = ≈0.9524

Find sin and tan . Write each answer as a decimal rounded to four decimal places. 45 B C 53 28 A

You can use your calculator to find a decimal approximation for trig ratios. Example 3: Use your calculator to approximate the given value to four decimal places. a) sin 82° b) cos 30° c) tan 60° Solutions: 0.9903 0.8660 1.7321

In summary, notice 4 things: The 2 acute angles of a right triangle are always complementary The sin, cos, and tan of congruent angles in similar triangles are always equal no matter the side lengths The sin and cos ratios of 2 complementary angles are always switched The tan ratios of 2 complementary angles are always reciprocals of one another

Homework: Page 159 (#1, 3, 7) and Page 166 (#2-14 even)