trigonometry

trig identities/sin cos tan/trig

what is the value of sin on the unit circle?

y

what is the value of cos on the unit circle?

x

what is the value of tan on the unit circle?

y/x

what is the value of csc on the unit circle?

1/y

what is the value of sec on the unit circle?

1/x

what is the value of cot on the unit circle?

x/y

when is the law of sines used?

aas, asa, ssa

what is the law of sines?

sin A/a = sinB/b = sinC/c

when is the law of cosines used?

sss, sas

what is the law of cosines for angles?

a²-b²-c² / -2(bc)

what is the law of cosines for sides?

a²=b²+c²-2ab*cosA

how do you convert from degrees to radians?

x * pi/180

how do you convert from radians to degrees?

x * 180/pi

how long are the legs on a 45-45-90 triangle?

x (they’re the same)

how long is the hypotenuse on a 45-45-90 triangle?

one leg * sqrt of 2

how long is the short leg on a 30-60-90 triangle?

x

how long is the long leg on a 30-60-90 triangle?

x * sqrt of 3

how long is the hypotenuse on a 30-60-90 triangle?

2x (short leg)

what is positive in the first quadrant?

all values (all)

what is positive in the second quadrant?

sin and csc (students)

what is positive in the third quadrant?

tan and cot (take)

what is positive in the fourth quadrant?

cos and sec (calculus)

what is the value of cos of theta?

x

what is the value of sin of theta?

y

what is the value of tan of theta?

y/x which is sin/cos

what is the value of sec of theta?

1/cos

what is the value of csc of theta?

1/sin

what is the value of cot of theta

x/y which is cos/sin

what is the pythagorean identity for cos and sin?

cos²(theta) + sin² (theta) = 1

what is the pythagorean identity for tan and sec?

tan²(theta) + 1 = sec²(theta)

what is the pythagorean identity for cot and csc?

1 + cot²(theta) = csc²(theta)