Trigonometry (Trig) unit Outline
trig 01-Identify trig ratios by sides (soh, cah, toa)
trig 02-given three sides of right triangle, find tan a, sin a, and cos a as ratios
Using our knowledge of the formulas above, we can apply them to find out the sine, cosine and tangent of A.
Sin A=3/5
Cos A=4/5
Tan A=3/4
Sin A=3/5
Cos A=4/5
Tan A=3/4
trig 03-given a special right triangle, find tan a, sin a, cos a. (30-60-90, 45-45-90) by hand (no calculator, exact, simplified radical answers)
trig 04-given an angle and side in a right triangle, find missing sides using algebra and calculator.
In this triangle, we know are given an angle, the hypotenuse as 12, and the opposite side as x. We can use sine to figure this problem out.
Example: Sine28=x/12
-By cross-multiplying, we would get x=Sin28(12)
-Next, you would plug this in to the calculator and get your answer:
x=5.6
Example: Sine28=x/12
-By cross-multiplying, we would get x=Sin28(12)
-Next, you would plug this in to the calculator and get your answer:
x=5.6
trig 05-find the area of a regular pentagon, octagon, dodecagon, using trig and a calculator. answers should be accurate/precise to the nearest 1/100th
We know the formula for finding the area of a regular polygon from the last unit is A=1/2*a*s*n
In this example to the right, we know two of the three components a=? s=10 n=5 If we focus on the single triangle, we can figure out the top angle by multiplying the number of sides by 2 to get 10 and divide that number (20) by 360 to get 36. Now we can just solve it as a tangent. The equation would be tan36=5/a (a stands for apothem) Using our exchange property of proportions we would get that a=5/tan36 Now we know all three components: a=5/tan36 s=10 n=5 Plugging these into the equation we would get A=1/2*5/tan36*10*5 A=125/tan36 A=172.05 |
trig 06-solve problems to find height using angle of elevation/depression using trig.
trig 07-given two sides, find missing angles using algebra and calculator
In this triangle, we are given the opposite and adjacent sides. We could use the formula for tangent.
It would be tan x=7/6
In the calculator, we would solve but use tan(-1).
7/6 * tan (-1) would be rounded to equal:
49 degrees
It would be tan x=7/6
In the calculator, we would solve but use tan(-1).
7/6 * tan (-1) would be rounded to equal:
49 degrees
trig 08-use trig identities to simplify expressions
The Trig identities we need to know for this unit are reciprocal, quotient, and pythagorean identities. They are:
trig 09-know and apply law of sines
trig 10-derive the law of sines
trig 11-know and apply law of cosines
trig 12-derive the law of cosines
trig 13-solve triangles. be able to determine whether 0,1,2 or infinitely many triangles can be formed with the given three pieces of information (angles and/or sides).
When choosing between law of sines and cosines, we use them in separate circumstances. For law of sines, we can use them in triangle conditions such as AAS, ASS, and ASA. We can use law of cosines in cases such as SSS and SAS.
Also, an infinite amount of triangles can be formed with AAA, 0,1, or 2 can be formed with ASS, and 1 can be formed with ASA, AAS, SAS, and SSS.
Also, an infinite amount of triangles can be formed with AAA, 0,1, or 2 can be formed with ASS, and 1 can be formed with ASA, AAS, SAS, and SSS.