13.4 and 13.5 Basic Trig

Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.

New Words Trigonometry: the study of the propertiesof triangles. Trigonometric ratio: ratio of the measures of 2sides of a triangle.

Sine: written sin, read [sahyn] Cosine: written cos, read [koh-sahyn] Tangent: written tan, read [tan- juhnt)

New sayings Some old horse, caught another horse, taking oats away. Signs of happiness come after having tankards of ale. Some of her children are having trouble over algebra. Some out houses can actually have totally odorless aromas. SOH CAH TOA (read soh-kuh-toh-uh)

Right Triangle Has 3 sides: Hypotenuse Adjacent Opposite The Hypotenuse is always across from the right angle. It is the longest. The other two will depend on what angle we are dealing with

The opposite side is across the triangle from the angle. The adjacent side is next to the angle. It is one of the sides of the angle.

Hypotenuse Adjacent Opposite If we are talking about this angle then...

Right Triangle Hypotenuse Adjacent Opposite If we are talking about this angle then...

Sine Sine is the ratio of the opposite side divided by the hypotenuse. B sin B = opp hyp 3 5 C sin C = opp hyp 4 5

Cosine Cosine is the ratio of the adjacent side divided by the hypotenuse. B cos B = adj hyp 4 5 C cos C = adj hyp 3 5

Tangent tangent is the ratio of the opposite side divided by the adjacent. B tan B = opp adj 3 4 C tan C = opp adj 4 3

What’s up with the sayings Some old horse, caught another horse, taking oats away. sin = opp hyp cos = adj hyp tan = opp adj

Which ever one you like... Some old horse, caught another horse, taking oats away. Signs of happiness come after having tankards of ale. Some of her children are having trouble over algebra. Some out houses can actually have totally odorless aromas. SOH CAH TOA (read soh-kuh-toh-uh) soak-a-toe-a

New Words Angle of depression Angle of elevation

Find tan j k 3 6 tan J = opp adj 3 6 jl 45

Find cos j k 3 6 cos J = adj hyp 6 45 jl now simplify

Find tan k k 5 12 tan K = opp adj 12 5 jl 13

Find sin k k 5 12 sin K = opp hyp jl

Find cos k k 5 12 cos K = adj hyp 5 13 jl

To find a side... What ratio can we use? 13 tan 30 = opp adj ? 13 ? 30 What sides do we know?.5774 X 13 = ?.5774= ? 13

To find a side... What ratio can we use? 210 cos 18 = adj hyp ? 210 ? 18 What sides do we know?.9511 X 210 = ?.9511= ? 210

To find an angle... What ratio can we use? 95 tan ? = opp adj ? What sides do we know? = tan = 67.17

To find an angle... What ratio can we use? 3078 sin ? = opp hyp ? 600 What sides do we know? =.1949 sin = 11.24

Make sure your calculator is in degrees not radians When calculating trig functions, we usually round to 4 decimal places