Trigonometry Lecture Notes_part1-1

# Trig functions and complements as mentioned above the

This preview shows pages 11–16. Sign up to view the full content.

Trig Functions and Complements: As mentioned above, the two non 90 ringoperator angles must add to 90 ringoperator . This makes them complementary. This means that the cosine of one of these angles will always equal the sine of the other angle and vice versa. You will also see this pattern on the unit circle I asked you to memorize. Let’s see why, consider the drawing below:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Consider the angles θ and B What is the sine of θ ? How does that compare with the cosine of B? (Notice that angle B = 90 ringoperator - θ ) The Cofunction Identities (note if using radian measure use 2 π instead of 90 ringoperator ) ( ) ( ) ( ) sin cos 90 tan cot 90 sec csc 90 θ θ θ θ θ θ = - = - = - ringoperator ringoperator ringoperator ( ) ( ) ( ) cos sin 90 cot tan 90 csc sec 90 θ θ θ θ θ θ = - = - = - ringoperator ringoperator ringoperator Example 12 Find a cofunction with the same value as the expression given: a. sin38 ringoperator b. csc 3 π Applications Many problems of right angle trigonometry involve the angle made with an imaginary horizontal line. The angle formed by that line and the line of sight to an object that is above the horizontal is called the angle of elevation . If the object is below the horizontal the angle is called the angle of depression .
Example 13 A surveyor sights the top of a Giant Sequoya tree in California and measures the angle of elevation to be 32 degrees. The surveyor is standing 275 feet away from the base of the tree. What is the height of the tree? 32 ringoperator 275 Example 14 A plane must achieve a minimum angle of elevation once it reaches the end of its runway which is 200 yards from a six story building in order to clear the top of the building safely. What angle of elevation must the plane exceed in order to clear the 60 ft tall building in its path? Section 6.2 Trig Functions of Any Angle

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Let θ be any angle in standard position, and let ( ) , P x y = be a point on the terminal side of θ . If 2 2 r x y = + is the distance from ( ) 0,0 to ( ) , x y , as shown below, the six trig functions of θ are defined as: sin csc , 0 y r r y y θ θ = = cos sec , 0 x r r x x θ θ = = tan , 0 cot , 0 y x x x y y θ θ = = Example 15 Let ( ) 2,5 P = - be a point on the terminal side of θ . Find each of the six trigonometric functions of θ .
Example 16 Find the sine function and the tangent function (if possible) at the following four quadrantal angles: a. 0 θ = b. 2 π θ = c. θ π = d. 3 2 π θ = Signs of the Trigonometric Functions Since the six trigonometric function all depend on the quantities x, y, and r and since r is always positive , the sign of a trigonometric function depends upon the quadrant in which θ lies. For example, in quadrant II we have angles of measures that are in the following set ( ) { } | 90 ,180 θ θ ringoperator ringoperator . This means that the sines of all of those angles are positive (since all y’s are positive in quad II), the cosines of all of those angles are negative (since all x’s are negative in quad II), and finally the tangents in quadrant II are always negative (since x and y have different signs).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern