Warm-Up: March 4, 2016 Find the exact value of cos sin −1 − 4 5

Homework Questions?

Right Triangle Trigonometry Section 4.3

Right Triangles B c = length of the hypotenuse A right triangle has a 90˚ angle and two acute angles B c = length of the hypotenuse a = length of side opposite of A, adjacent to B A C b = length of side adjacent to A, opposite of B

Trigonometric Functions SOH-CAH-TOA

More Trigonometric Functions

Example 1 Find the value of each of the trigonometric functions of θ. 3 4 c A B C θ

You-Try #1 Find the value of each of the trigonometric functions of θ. 5 12 c A B C θ

Pythagorean Triples Pythagorean triples are integer side lengths of a right triangle 3-4-5 5-12-13 7-24-25 8-15-17 And many more And any multiple of any of them (such as 6-8-10)

Special Triangles

Trig Values of Special Angles Degrees Radians sin cos tan 30˚ 45˚ 60˚

You-Try #2 Find the exact value of sin 𝜋 6 − cos 𝜋 4

Inverse Trig Functions If sin 𝜃 =𝑥, then 𝜃= sin −1 𝑥 “Theta equals the inverse sine of x” Other inverse trig functions follow the same format TI-83: [2nd] [sin]

You-Try #3 Use a calculator to find the value of the acute angle 𝜃 to the nearest tenth of a degree. cos 𝜃 =0.8771 tan 𝜃 =26.0307 Use a calculator to find the value of the acute angle 𝜃 in radians, rounded to three decimal places. sin 𝜃 =0.9499 tan 𝜃 =0.5117

Assignment Page 461 #1-19 odd No calculator

First Few Problems B B 3) 29 9 θ A θ C 12 A C 21 5) B 26 10 θ A C In Exercises 1-8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then, find the value of each of the six trigonometric functions of θ. 3) 21 29 A B C θ 9 12 A B C θ 1) 10 5) 26 A B C θ

Warm-Up: Find the value of each of the trigonometric functions of θ. a 15 17 A B C θ

Homework Questions?

Unit Circle Quiz! Clear everything off of your desk except a pencil and eraser. 5 minute time limit All or nothing Must be turned in by the end of 5 minutes Do NOT begin until instructed to do so. Any talking while any quiz is out will result in a zero.

Cofunctions The value of a trig function of an angle is equal to the value of the cofunction of the complement of the angle If θ is in radians, replace 90˚ with

Example 4 Find a cofunction with the same value as the given function.

You-Try #4 Find a cofunction with the same value as the given function.

Trig Functions on TI-83 All scientific and graphing calculators should have buttons for sin, cos, and tan. Most do not have csc, sec, and cot. Make sure that your calculator is set to the correct angle measure (degrees or radians) TI-83: Press [MODE] and make sure the correct one of “Radian” or “Degree” is highlighted

Angles of Elevation & Depression The angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is the angle of elevation. The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is the angle of depression. angle of depression

Example 5 Sighting the top of a building, a surveyor measured the angle of elevation to be 24˚. The transit is 5 feet above the ground and 250 feet from the building. Find the building’s height (to the nearest foot).

You-Try #5 At a certain time of day, the angle of elevation of the sun is 39˚. A tree casts a shadow 37 feet long. Find the tree’s height (to the nearest foot).

Assignment Read Section 4.3 Page 461 #1-19 odd Page 462 #29-49 odd No calculator Page 462 #29-49 odd Calculator required

First Few Problems In Exercises 21-28, find a cofunction with the same value as the given expression.

Warm-Up: At a certain time of day, the angle of elevation of the sun is 59˚. A tree casts a shadow 24 feet long. Find the tree’s height (to the nearest foot).

Homework Questions?

Unit Circle Quiz! Clear everything off of your desk except a pencil and eraser. 5 minute time limit All or nothing Must be turned in by the end of 5 minutes Do NOT begin until instructed to do so. Any talking while any quiz is out will result in a zero.

Unit Circle Quiz! Clear everything off of your desk except a pencil and eraser. 5 minute time limit

Example 6 The Washington Monument is 555 feet high. If you stand ¼ mile away (1320 feet), and look at the top, what is the angle of elevation (to the nearest degree)?

You-Try #6 A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

Assignment Read Section 4.3 Page 461 #1-19 odd Page 462 #29-49 odd No calculator Page 462 #29-49 odd Calculator required