Unit Circle
The coordinates of pi/3 are:
What is (1/2, sqrt3/2)
Draw a right triangle on the unit circle with a theta of pi/3. Using SOH CAH TOA, calculate the length of the legs and therefore the coordinates.
radians are
what is a unit of measure for angles based on the radius of circles?
csc is equal to
what is 1/sin?
- trig identities
The R in QSFR
What is Reference angle
The radian value at (-1,0)
What is pi
Since (-1,0) is halfway around the circle, and the full unit circle is 2pi, its just pi.
Convert 180 degrees into radians.
What is pi?
Divide by 180/pi.
sec^2theta - 1 is equal to
Change sec to 1/cos, distribute, cos/cos=1, using Pythagorean Identity
using QSFR
What is finding the exact value of trigonometric functions?
The diameter of a unit circle
What is 2?
The radius of a unit circle is 1, so the diameter is 1x2.
convert 2pi/3 to degrees.
What is 120 degrees?
Multiply 2pi/3 by 180/pi.
Make cos(sec-cos) into one identity
What is sin^2 theta?
Change sec to 1/cos, distribute cos/cos=1, using Pythagorean identity
The reference angle of tan 7pi/4
What is pi/4?
7pi/4 is pi/4 less than 8pi/4, which is (1,0), making pi/4 the reference angle
Cot is positive in these quadrants
What is QI and QIII?
In QI, sin and cos are both positive and in QIII they are both negative. Since cot is cos/sin, those values of sin and cos lead to a positive cot value.
30 degrees in radians
what is pi/6?
Make (sin*cos)(1-cos^2) into one identity
What is cot?
Using Pythagorean identity change 1-cos^2 into sin^2, get rid of sin innumerator and one sin in denominator, left with cos/sin which = cot
the sign of csc 5pi/3
what is negative?
5pi/3 falls in the fourth quadrant, where csc, or 1/sin, is negative.