The Trigonometric Functions we will be looking at SINE COSINE TANGENT

The Trigonometric Functions SINE COSINE TANGENT

SINE Pronounced “sign”

Pronounced “co-sign” COSINE

Pronounced “tan-gent” TANGENT

Pronounced “theta” Greek Letter  Represents an unknown angle

opposite hypotenuse adjacent hypotenuse opposite adjacent

Finding sin, cos, and tan. Just writing a ratio.

Find the sine, the cosine, and the tangent of theta. Give a fraction Shrink yourself down and stand where the angle is. Now, figure out your ratios.

Find the sine, the cosine, and the tangent of theta Shrink yourself down and stand where the angle is. Now, figure out your ratios.

Using Trig Ratios to Find a Missing SIDE

To find a missing SIDE 1. Draw stick-man at the given angle. 2. Identify the GIVEN sides (Opposite, Adjacent, or Hypotenuse). 3. Figure out which trig ratio to use. 4. Set up the EQUATION. 5. Solve for the variable.

1. Problems match the WS. H A Where does x reside? If you see it up high then we MULTIP LY!

2. Problems match the WS. H O Where does x reside? If X is down below, The X and the angle will switch… SLIDE & DIVIDE

3. Problems match the WS. H A

Steps to finding the missing angle of a right triangle using trigonometric ratios: 1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle  5.92 km HYP OPP ADJ 2.67 km

Steps to finding the missing angle of a right triangle using trigonometric ratios: 2. For the unknown angle choose the correct trig ratio which can be used to set up an equation 3. Set up the equation  5.92 km HYP OPP ADJ 2.67 km

Steps to finding the missing angle of a right triangle using trigonometric ratios: 4. Solve the equation to find the unknown using the inverse of trigonometric ratio.  5.92 km HYP OPP ADJ 2.67 km

Your turn Practice Together: Find, to one decimal place, the unknown angle in the triangle.  3.1 km 2.1 km

YOU DO: Find, to 1 decimal place, the unknown angle in the given triangle.  7 m 4 m

Sin-Cosine Cofunction

The Sin-Cosine Cofunction

1. What is sin A? 2. What is Cos C?

3. What is Sin Z? 4. What is Cos X?

5. Sin 28 = ?

6. Cos 10 = ?

7.  ABC where  B = 90. Cos A = 3/5 What is Sin C?

8. Sin  = Cos 15 What is  ?

Trig Application Problems MM2G2c: Solve application problems using the trigonometric ratios.

Depression and Elevation horizontal line of sight horizontal angle of elevation angle of depression

9. Classify each angle as angle of elevation or angle of depression. Angle of Depression Angle of Elevation Angle of Depression Angle of Elevation

Example 10 Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation to the nearest degree? 5280 feet – 1 mile

Example 11 The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder? Round to the nearest whole number.

Example 12 Find the angle of elevation to the top of a tree for an observer who is 31.4 meters from the tree if the observer’s eye is 1.8 meters above the ground and the tree is 23.2 meters tall. Round to the nearest degree.

Example 13 A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the building? Round to the nearest degree.

Example 14 A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from the boat and swims 935 feet to reach the wreck. What is the angle of depression from the boat to the shipwreck, to the nearest degree?

Example 15 A 5ft tall bird watcher is standing 50 feet from the base of a large tree. The person measures the angle of elevation to a bird on top of the tree as 71.5°. How tall is the tree? Round to the tenth.

Example 16 A block slides down a 45  slope for a total of 2.8 meters. What is the change in the height of the block? Round to the nearest tenth.

Example 17 A projectile has an initial horizontal velocity of 5 meters/second and an initial vertical velocity of 3 meters/second upward. At what angle was the projectile fired, to the nearest degree?

Example 18 A construction worker leans his ladder against a building making a 60 o angle with the ground. If his ladder is 20 feet long, how far away is the base of the ladder from the building? Round to the nearest tenth.