PRO Trig Flashcards
What function can be placed over one to get csc?
Sin
What function can be placed over one to get sec?
Cos
What function can be placed over one to get cot?
What functions can be placed over each other to get cot?
Tan, Cos/Sin
What function can be placed over one to get sin?
Csc
What function can be placed over one to get cos?
Sec
What function can be placed over one to get tan?
What functions can be placed over each other to get tan?
Cot, Sin/Cos
What is the first “Pythagorean” identity?
Sin^2 + Cos^2 = 1
How do you get the second and third “Pythagorean” identities?
Divide by Sin^2 and Cos^2
What are sin, cos, and tan in terms of x and y? (On the unit circle)
Sin=Y, Cos=x, and Tan=y/x
What is sin(-t)?
-Sin(t)
What is cos(-t)?
Cos(t)
What is tan(-t)?
-Tan(t)
What is sin(a+b)?
Sin(a)Cos(b) + Cos(a)Sin(b)
What is sin(a-b)?
Sin(a)Cos(b) - Cos(a)Sin(b)
What is cos(a+b)?
Cos(a)Cos(b) - Sin(a)*Sin(b)
What is cos(a-b)?
Cos(a)Cos(b) + Sin(a)*Sin(b)
What is tan(a+b)?
(Tan(a)+Tan(b))/(1-Tan(a)*Tan(b))
What is tan(a-b)?
(Tan(a)-Tan(b))/(1+Tan(a)*Tan(b))
What is Sin(2a)?
2Sin(a)Cos(a)
What is Cos(2a)?
Cos^2(a)-Sin^2(a), which you can use the first P identity to get 1-2Sin^2(a) or 2Cos(a)^2-1
What is Tan(2a)?
(2*Tan(a))/(1-Tan(a)^2)
What is Sin(a/2)?
+/- The square root of (1-Cos(a))/2
What is Cos(a/2)?
+/- The square root of (1+Cos(a))/2
What is Tan(a/2)?
+/- The square root of (1-Cos(a))/(1+Cos(a)) which is equal to (1-Cos(a))/Sin(a) or Sin(a)/(1+Cos(a))
What is Sin(x) + Sin(y)? (Might not need to know)
2Sin(x+y over 2)Cos(x-y over 2)
What is Sin(x) - Sin(y)? (Might not need to know)
2Sin(x-y over 2)Cos(x+y over 2)
What is Cos(x) + Cos(y)? (Might not need to know)
2Cos(x-y over 2)Cos(x+y over 2)
What is Cos(x) - Cos(y)? (Might not need to know)
-2Sin(x-y over 2)Sin(x+y over 2)
What is Sin(x)*Cos(y)? (Might not need to know)
.5[Sin(x+y)+Sin(x-y)]
What is Cos(x)*Sin(y)? (Might not need to know)
.5[Sin(x+y)-Sin(x-y)]
What is Cos(x)*Cos(y)? (Might not need to know)
.5[Cos(x+y)+Cos(x-y)]
What is Sin(x)*Sin(y)? (Might not need to know)
.5[Cos(x-y)-Cos(x+y)]
What is the period of the normal sin and cos graphs?
2pie
What is the period of tan and cot?
Pie
What is the period of sec and csc?
2pie
What is the amplitude of any trig function?
Tan, Cot, Sec, and Csc have no amplitude, the amplitude of sin and cos is the (absolute value of the) number in front of the function
What is the formula for the period of a trig function?
regular period/the absolute value of the number inside the parenthesis of the function
What is the phase shift of Trig(x+pie)?
Pie to the left
What is the phase shift of Sin(Bx-C)?
C/B to the right
What is the sin rule?
Sin(A)/a = Sin(B)/b = Sin(C)/c
What is the cos rule?
The Opposite Side^2=Side^2 + Side^2 - 2sideside*Cos(angle)
How do you find the area of a triangle using the sine rule?
1/2 * a * b * Sin(C)
What is the point associated with 0*?
(1,0)
What is the point associated with 30* or pie/6?
(Square root of 3 over 2, 1/2)
What is the point associated with 45* or pie/4?
(Square root of 2 over 2, “”)
What is the point associated with 60* or pie/3?
(1/2, Square root of 3 over 2)
What is the phrase used with trig functions and right triangles?
SOH-CAH-TOA
How do you convert between radians and degrees?
pie/180*
What are the values of the sides of a 45* right triangle?
1,1,Square root of 2
What are the values of the sides of a 30* right triangle?
1,2,Square root of 3
What is Sin(90*-t)?
Cos(t)
What is Tan(90*-t)?
Cot(t)
What is Sec(90*-t)?
Csc(t)
What is Cos(90*-t)?
Sin(t)
What is Cot(90*-t)?
Tan(t)
What is Csc(90*-t)?
Sec(t)
What is Tan(30*)?
Square root of three over 3
What is Tan(45*)?
1
What is Tan(60*)?
Square root of three
What Quadrants does Sin-1 need to be restricted to?
1 and 4
What Quadrants does Cos-1 need to be restricted to?
1 and 2
What Quadrants does Tan-1 need to be restricted to?
1 and 4
What is the way to find out the area of a triangle given each side?
The square root of s(s-a)(s-b)*(s-c)
s=(a+b+c)/2
