When listening to Mr. Burger on how to prove trig identities he stated that you mightwant to work with both sides and come to common end statement. I think of proving trigidentities the same way you did proofs in geometry. You typically want to work with oneside, massage it, and hopefully you will create the expression on the other side of theequal sign. These types of problems should be viewed as ‘given a problem and itsanswer, how do you get to the answer?’. You want to keep in mind all of the trigidentities you have been exposed to thus far to assist you in proving trig identities. Example

Prove:1tantan1cot
θ θ θ
+=+
By examining both sides of the equal sides, it appears that you want to begin with the leftside in order to create the right side.sin11tancoscos1cot1sin θ θ θ θ θ θ
++=++
=cossincoscossincossinsin
θ θ θ θ θ θ θ θ
++
=cossincossincossin
θ θ θ θ θ θ
++
=cossinsincoscossin
θ θ θ θ θ θ
+ +
÷
=cossinsincossincos
θ θ θ θ θ θ
++
·
=sintancos
θ θ θ
=
The reason why it was best to convert in terms of sine and cosine is because the resultanttan θ
is a trig function that can be expressed that way. There will be times when you willhave to begin with the right side of the equal sign and work your way to create the leftside of the equal sign.

Try the following:
Prove.1.

1cossintancos
x x x
− =
2.

cottanseccsc
α α α α
+ =
3.

2222
sectan122sin2cos
θ θ θ θ
−=+
Answers:
2
11coscoscoscoscos
x x x x x
− = −
=
2
1coscos
−
=
2
sincos
x
=sinsinsinsintansinsintancoscos
x x x x x x x x x x
= = =
cossincottansincos
α α α α α α
+ = +
=
22
cossinsincossincos
α α α α α α
+
=
22
cossin111cscsecsincossincossincos
α α α α α α α α α α
+= = ⋅ =
= sec
α
csc
α

...PROVINGIDENTITIESProvingIdentitiesProving an identity is simply verifying that one member of the equation is identically equal to the other member. It is important to know that there is no general rule in proving an identity. The proper choice of the fundamental identities and algebraic operations will certainly make the verification process easier. Mathematical competence and familiarity with the fundamental identities are the basic tools that will greatly facilitate the transformations involved in proving an identity. Finally, facility in provingidentities can be greatly obtained through constant practice.
Ms. Juliet Juliana A. Buenaventura UST Faculty of Pharmacy
Suggestions in ProvingIdentities
Start with the more complicated side and transform it to the simpler form on the other side. It may be more convenient to transform each side separately into the same equivalent form. Often it is desirable to convert an expression to one containing the sine and cosine.
Suggestions in ProvingIdentities
It may be advantageous to convert an expression to one involving only a single function, provided no radicals are introduced. Consider the possibilities of applying algebraic processes (multiplying, factoring,...

...Ashley Washington
Final exam essay
6/2/14
Six Trigonometric functions
The six trigonometric functions are found in a right triangle because they contain a right angle. The measures of the three angles, labeled A, B, and C. we used lower case letters a, b, and c to denote the lengths of the sides opposite of angles A, B, and C respectively. These six trigonometric functions are sine, cosine, and tangent, which are often used the most. The other three are cotangent, secant, and cosecant. However, it is said that in a right triangle the trigonometric ratios the sine, the cosine, and so on are functions of the acute angle. They depend only on the acute angle. For example, each value of sin theta represents the ratio of the opposite side to the hypotenuse, in every right triangle with that acute angle. If angle theta is 28 degrees, so then in every right triangle with a 28 degrees angle, its sides will be in the same ratio. We read it as, Sin. 28 degrees equals .469. This means that the right triangle have an acute angle of 28 degrees, which is half of the opposite angle. On the other hand, these six trigonometric functions have different labels names for each side. For example, the side label lower case “c” has a special name because it is the side opposite of the right angle capital letter “C”. This is called, “hypotenuse”. If we have angle capital letter “B” the side label lower case “b” will be...

...computer graphics, geophysics, crystallography and economics , some things in these fields cannot be understood without trigonometry. These proved that trigonometry really is needed in our real life situation.
Trigonometry finds a perfect partner in modern architecture. It is really needed in architecture fields, without trigonometry architecture is hard to understand. The beautifully curved surfaces in steel, stone and glass would be impossible if not for the immense potential of this science. So how does this work actually. In fact the flat panels and straight planes in the building are but at an angle to one another and the illusion is that of a curved surface.
Although it is unlikely that one will ever need to directly apply a trigonometric function in solving a practical issue, the fundamental background of the science finds usage in an area which is passion for many is music. As we may be aware sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry.
Besides that, trigonometry is an arty science that can be used to measure the heights of mountains....

...TrigonometricIdentities
I. Pythagorean Identities
A. [pic]
B. [pic]
C. [pic]
II. Sum and Difference of Angles Identities
A. [pic]
B. [pic]
C. [pic]
D. [pic]
E. [pic]
F. [pic]
III. Double Angle Identities
A. [pic]
B. [pic]
=[pic]
=[pic]
C. [pic]
IV. Half Angle Identities
A. [pic]
B. [pic]
C. [pic]
6-1 Inverse Trig Functions p. 468: 1-31 odd
I. Inverse Trig Functions
A. [pic]
B. [pic]
C. [pic]
Find the exact value of each expression
1. [pic] 2. [pic] 3. [pic]
4. [pic] 5. [pic] 6. [pic]
Use a calculator to find each value.
7. [pic] 8. [pic] 9. [pic]
Find the exact value of each expression.
10. [pic] 11. [pic] 12. [pic]
6-2 Inverse Trig Functions Continued p. 474:1-41 odd
I. Inverse Trig Functions
A. [pic]
B. [pic]
C. [pic]
Find the exact value of each expression.
1. [pic] 2. [pic] 3. [pic]
4. [pic] 5. [pic] 6. [pic] 7. [pic]
Find the exact value of each.
8. [pic] 9. [pic] 10. [pic]
Use a calculator to find each value.
11. [pic] 12. [pic]
TrigonometricIdentities Trig Identities Worksheet: 1-6...

...Section 5.2 Trigonometric Functions of Real Numbers
The Trigonometric Functions
EXAMPLE: Use the Table below to ﬁnd the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2
1
EXAMPLE: Use the Table below to ﬁnd the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2 Solution: (a) From the Table, we see that the terminal point determined by √ t = √ is P (1/2, 3/2). Since the coordinates are x = 1/2 and π/3 y = 3/2, we have √ √ π 3 3/2 √ π 1 π sin = cos = tan = = 3 3 2 3 2 3 1/2 √ √ π 3 2 3 π π 1/2 csc = = sec = 2 cot = √ 3 3 3 3 3 3/2 (b) The terminal point determined by π/2 is P (0, 1). So π π 1 π 0 π cos = 0 csc = = 1 cot = = 0 sin = 1 2 2 2 1 2 1 But tan π/2 and sec π/2 are undeﬁned because x = 0 appears in the denominator in each of their deﬁnitions. π . 4 Solution: √ From the Table above, we see that √ terminal point determined by t = π/4 is the √ √ P ( 2/2, 2/2). Since the coordinates are x = 2/2 and y = 2/2, we have √ √ √ π 2 2 2/2 π π sin = =1 cos = tan = √ 4 2 4 2 4 2/2 √ π √ π π √ 2/2 csc = 2 sec = 2 cot = √ =1 4 4 4 2/2 EXAMPLE: Find the six trigonometric functions of each given real number t =
2
Values of the Trigonometric Functions
EXAMPLE: π π (a) cos > 0, because the terminal point of t = is in Quadrant I. 3 3 (b) tan 4 > 0, because the terminal point of t = 4 is in Quadrant III. (c) If cos t < 0 and...

...Identity refers to the construction of individual and society's characteristics by which we are symbolized and recognised as to who we are. In this assignment I intend to explore the meaning of identity. In considering the link between personal and social, I will examine the process of identity formation, and discuss the extent in which we are able to control and shape our own identities.
The definition of identity has been contested by many social scientists, as it has many influences, which has to be considered, such as, gender, social class, nationality, physical appearances, religious and ethnicity. Initially, we acquire some aspects of identity through official documents, such as birth certificate, where in order to exit, a birth must be registered and categorized by name and gender, which can never be legally changed and influence our entire identity formation, as to the expected manner within feminine and masculine characteristics (Woodward, 2004, p.44). For instance, Madan Sarup uses passports from different stages of his life to convey some aspects of his identity. All three passports reveal his name, gender and categorized him as to what nation he belongs to, which suggests continuity in his identity. Furthermore, the passports also reveal his physical appearance, which changes with age. The question 'which is the real you?' by Sarup's...

...My identity: Stress resistance.
If you asked me about myself, I would respond without any doubt, “I am Britney, a stress resistant person.” I think maintaining full control over your emotional response to life's complications plays an important role in the way your day is shaped, and that of others. Confidence in one's abilities and a clear mind gives way to more calculated decisions, rather than falling victim to a potentially hectic environment. According to Dr. Keith Horinouchi, “stress resistance” means “the body’s ability to handle everyday stresses, preferably through a healthy lifestyle.” Now, stress resistance is my motto, which always reminds me how I should react to any difficulties that I face on my life's path. However, I was not always this way. I would say that this is a skill that I have slowly developed over the course of my life. Stress resistance is what helps me in every difficult situation.
My mother was twenty-seven when she had me, and she always wanted a daughter. When I came to this world, my parents were the happiest people ever. They were always with me: bringing me up, playing with me and spending all of their free time on me. Unfortunately, I did not have any brothers and sisters around to play with me. When I played, I easily grew bored because I could not keep myself entertained alone, and because of that, I was stressed. I spent a fair amount of my childhood without many companions my age. However, I had two friends, (who...

...Rough Draft
It’s funny to think how different I would be without some major characteristics of my life. For example, if my grandpa had still been alive when I was born I most likely would have a few qualities that I am missing today. Since he was a sailor, he was resilient and rough around the edges. I’ve always been more sweet and sensitive, and if he had been around to influence me his traits may have passed along to me. My grandpa also worked near asbestos, so if he wouldn’t have died before I was born, he would have had serious health problems while I was alive. So far in my life, I’ve never had to deal with having an ill family member, thus I haven’t developed the strength to handle a situation involving sick relatives. Also, if I would have known my grandpa while he was sick, I would have seen a softer side of my dad. I have always seen my dad as strong and influential, and he pushes me to try my hardest at everything I do. If I would have seen him break when his dad was sick, I may not have the same perspective or relationship with him that I have now, because I would lose part of the reverence I have now for his strength, and he most likely wouldn’t be as influential on me. My dad’s motivation is what developed my strong work ethic, and my work ethic influences my actions every day. Once all the dots are connected, if it wasn’t for my grandpa’s early death I could not only have a different perspective of my dad, but also may not have the strong work ethic I have...