Trig Quiz (4.3)

reference angle symbol

"r" or theta (can be confused with radius)

if tan = 2, what is the adjacent measure? #33 page 8 hw

1 because 2 = 2/1

what are the radian families and what do these mean?

1) quadrantal (0,90,180,270,360) 2) pi/4 (45 degrees) 3) pi/6 (30 degrees) 4) pi/3 (60 degrees) these mean that if an angle has a denominator of 4, 6, or 3, its reference angle will be pi/4, pi/6, or pi/3 (match its family)

what do reciprocals mean?

1/x so csc would be 1/sin

to find the reference angle of an OG angle in the 2nd quadrant, what should you do (for both in degrees and in radians)?

180 - theta pi - theta

to find the reference angle of an OG angle in the 4th quadrant, what should you do (for both in degrees and in radians)? * For this card and the previous 2, you will never subtract/add from 90 or 270, it's always from either 180 (pi) or 360 (2pi) *

360 - theta 2pi- theta

what quadrant is cos(4pi/3) in?

3rd the reference angle (pi/3) will be in the 3rd quadrant too

what is the reference angle of -405 degrees?

45 405-360 = 45

reference angles are always ________ and _______

POSITIVE and acute (even if OG angle is negative)

csc(11pi/6) is not -1/2. why?

SWITCHES (1/sin)

what should you remember to put on your answer?

UNITS (degrees or radians)

draw signs of trig functions on a circle

all students text constantly

what are quadrantal angles?

angles whose terminal side is on an axis (multiples of 90)

negative angles go _____ and positive angles go ________

clockwise ; counterclockwise

what are the angles 0 and 360 called and why?

coterminal bc in same place

what mode should your calculator be in?

degree

what is the easiest way to solve sohcahtoa of any angle?

draw it wherever it is, label the reference angle, label the sides (with neg/pos), and solve

going off of previous card, when in doubt of a problem, what can you do? #30 on page 8 hw

draw where the angle is and label

going off the previous card, what if two are negative?

has to be the quadrant where the remaining trig is positive (can't all be negative)

when making your xyr triangle, what should you make sure you remember to label?

if x and y are negative or positive

if you are determining which quadrant tan theta = -2/3 and sine theta = negative is in, what should you do?

just look at negative part of tan (ignore 2/3) and see which quadrant both tan and sine are negative in

when solving for either sine of an angle on the unit circle, what should you do?

look at the y coordinate of that angle (ex: if finding sin270, it would be -1)

when finding the coordinates of a point on a triangle and it ends up being one of the special right triangles, will the points be the same as on a special right triangle? example 10 on page 23 notes & #73 on page 8 hw

not always unless the sides given are the same as on a special right triangle if they are not the same, you should set up a proportion and cross-multiply

the radius is always _______ on the xyr triangle

positive

if two of the sohcahtoa's are positive, what quadrant does the angle have to be in?

quadrant 1

on #73 page 8 hw, the 5 represents the ________

radius

what should you remember to do when for example you have a fraction and square root (8 square root of 2 divided by 4) #35 pg 8 hw

reduce/simplify

going off of previous card, what should you made sure and do when solving for sohcahtoa? "Check for Understanding" at bottom of page 23 notes

see if negative or positive

if a reference angle is 30, 45, or 60 degrees, what should you use?

special right triangles & solve (sohcahtoa)

to find the reference angle of an OG angle in the 3rd quadrant, what should you do (for both in degrees and in radians)?

theta - 180 theta - pi

t/f: on the all students text constantly circle, the placements of the trig functions are the same as their reciprocals ex: if sine is positive in the 2nd quadrant, so is cosecant

true

t/f: tan = sin/cos

true

t/f: cos540 = cos180

true 540 = 360 +180 (same kinda scenario as previous card)

t/f: for the xyr triangle, the x,y, and r will be 0, 1, or -1 for a quadrantal angle/on a unit circle

true it can change if not quadrantal or special right (ex: y could be 6 or something if not quadrantal, but it'll be given to you in the problem if not quadrantal or special right)

t/f: sin720 = sin360

true 720 = 360 times 2 but would not be 2 times sin360, it would just be the same

if a problem is given in degrees, what should you answer be in? what about if given in radians?

units in answer should be same as units in question (if given in radians, answer should be in radians and same for degrees)

for finding a reference angle given in radians, what should you do? #19 page 8 hw

use pi instead of degrees ex (#19): if it's (7pi/12) you would minus that from pi to get (5pi/12)

going off of the previous card, if an angle is quadrantal, what should you do?

use the unit circle and your xyr triangle and solve (sohcahtoa)

when doing pythagorean theorem for the xyr triangle, what should you do?

when solving, make all numbers positive and then if they are negative on the triangle, label them as negative

when is an expression (cos,sin,tan) undefined?

when you divide by 0

what axis does the reference angle touch?

x axis

cos =

x/r

USING THE XYR TRIANGLE, what does sin =

y/r

tan =

y/x

when finding the coordinates of a point on a triangle and it ends up being a 45,45,90 triangle, will x=y (basically will the x and y coordinates be the same)? example 10 on page 23 notes

yes because isosceles (1 across and 1 down)