HPC: Trig Functions

When you don't have a (b(x +/- c)) in your equation, how do you graph trig functions?

Factor a number out so you have a "b" value.

How do you graph trig functions when there is no distinct "b" value ("bx +/- c" is in the equation)?

Factor out a "b" in the equation before graphing.

How do you take a trig function OF a trig function?

Find the trig function in the parentheses, then use that answer.

When should you use Law of Sines VERSUS the Law of Cosines to solve a triangle? (in terms of lengths/angles GIVEN)

Law of Sines - ASA, AAS Law of Cosines - SSS, SAS

How do you calculate period of sin/cos functions?

(2pi/b)

How do you calculate period for tan/cot graphs?

(pi/b)

How do you convert radians to degrees?

1. Multiply by (180/pi) 2. Use "chunks" out of 180 (ex. (pi/3) has 3 chunks per 180 degrees, so 180/3 is 60 degrees)

How do you convert degrees to radians? (2 ways)

1. Multiply by (pi/180) 2. Use "chunks" out of 180 (ex. 60 degrees has 3 chunks go into 180, 60 is one chunk, so the radian measure is (pi/3))

How many radians are in a circle?

2π

Vocab: Midline of a Function

A horizontal line that divides a function where half of it is on top and half is below it.

For tan/cot graphs, where are the horizontal asymptotes?

After every period.

What are the three alternative trigonometric ratios? How do you remember them?

All the alternative ratios are the reciprocals of one of the main ratios. "csc" and "sec" are reciprocals of the OPPOSITE ratios their abbreviation starts with (ex. csc = 1/SINE).

How do you draw secant/cosecant graphs?

Draw the corresponding sine/cosine graph, and then draw parabolas at the crests and dips. Don't forget about horizontal asymptotes, but it's not required to draw them.

How do you find exact values of a degree/radian without a calculator?

Find the reference angle of the angle given, and use that to find the angle, given that the hypotenuse if extending out from the reference angle so that it works. Don't forget negatives if a leg is extending left/down.

When you find the inverse trig function of something, how do you know what the angle measure of the angle is?

From the x-axis to the terminal side. Make sure that the answer doesn't go through quadrants where the answer doesn't exist!

When solving for trigonometric ratios of special right triangles, what must you remember?

If there is a square root in the bottom of the fraction, you have to rationalize.

What does a negative a value do to a tan/cot graph?

It makes a positive graph negative and a negative graph positive (basically switches it from tan to cot and vice versa).

What does a negative a value do to a sin/cos graph?

It reflects the graph over the x-axis. Ex: A cosine graph that started at 1 starts at -1.

In the unit circle, positive angles travel _______ and negative angles travel ________.

Positive angles travel counter-clockwise, negative angles travel clockwise.

When answering inverse trig problems, you should always answer in _______.

Radians.

Trigonometric ratios only work with _______ triangles.

Right (have one 90 degree angle)

Sin graphs start at _; Cos graphs start at _.

Sin graphs start at (or the midline); Cos graphs start at 1 (or the amplitude from the midline).

Tan graphs are ________, and Cot graphs are ______.

Tan graphs are positive, and Cot graphs are negative.

Tan graphs go through (____,0); Cot graphs go through (___, 0).

Tan graphs go through (0,0), Cot graphs go through (pi/2, 0).

What is the angle of depression?

The angle formed by an observer's line of sight (a horizontal line) and his/her line of sight to an object below.

What is the angle of elevation?

The angle formed by an observer's line of sight (horizontal line) to an object above.

What does it mean when two angles are coterminal?

They end in the same place in the unit circle, but got there in a different way (ex. 45 degrees = -315 degrees)

How do you check exact values for trig functions?

Use the "All Students Take Calc" acronym to check if the answers you find are positive in the correct spots.

How do you do an exact value for multiples of 90 degrees?

Use the x/r/y diagram of a triangle that Swanson put in your notes where x is the horizontal value, and y is the vertical value. Put negatives where needed, then use the x/r/y functions of the notes triangle with your numbers (even though it isn't actually a triangle). Examples in pic!

How do you find exact values of inverse trig functions?

Using the answer for the inverse trig function, find side lengths in the correct QUADRANTS that satisfy the answer by working backwards.