The Unit Circle
Convert an angle from degree measure to radian measure and vice versa.
26 degrees to ___ radians
1.38 radians to ___ degrees
26 degrees to .45 radians
1.38 radians to ~79 degrees
Determine the exact value of trig functions for all ‘special angles’ (multiples of 30 or 45 degrees) on the Unit Circle.
Find the sin value for the following special angles:
45, 90, 120, 180
pi/4, pi/2, sqrt(3)/2, 1
Use basic trigonometric identities to simplify trigonometric expressions.
Simplify the following expression
cot(x)sin(x)
cos(x)
List the exact trigonometric ratios for the acute angles of any right triangle.
What are the ratios for the main two special triangles?
30 : 60 : 90
45 : 45 : 90
Determine coterminal angles for a given angle.
What are the coterminal angles for the following degrees :
1) 45 degrees
2) 120 degrees
1) 405 degrees / -315 degrees
2) 480 degrees / -240
Determine the exact value of a trigonometric function given a special angle.
List the sin and cosine for the special angle of 30 degrees
sin: 1/2
cos: sqrt(3)/2
Verify trigonometric identities by rewriting the identity in terms of sine and cosine.
Rewrite the equation in terms of sin to verify it.
cot(x)sec(x)=csc(x)
1/sin=1/sin
Determine the arc length or sector area of a circle given a radius and angle measure.
Determine the arc length of a section of a circle with 45 degrees and a radius of 12.
3 pi
(45/360)(12(2)pi)
Determine the exact value of expressions with inverse trigonometric functions at special angles.
Determine the value of: arcsin(sqrt(2)/2)
arcsin(sqrt(2)/2) = pi/4
Make designated trigonometric substitutions and simplify the resulting expressions.
Simplify the following function.
sec(x)sin^2(x)/1+sec(x)
1/cos^2
Draw one complete cycle of the basic sine and cosine non-translated graphs.
Determine the radius of a circle given an angle measure and arc length or sector area.
Determine the radius of a circle whose arclength measure 5 meters with an angle of 60 degrees
12.5/pi
(60/360)/(5pi/2)
Determine the exact value of a trigonometric function given the value of another trigonometric function at the same angle and sufficient information to determine the location of the angle.
Find another angle between 0 and 360 degrees that has the same value as the following angles:
1)Sin(290)
2)Cos(310)
3)Sin(120)
2) Cos(50)
3) Sin(60)
Use the sum and difference formulas to determine exact values of trigonometric expressions and verify identities.
Find the value of cos(pi/3-pi/4)
sqrt(4)+sqrt(6)/4
Given the equation of a sine/cosine function,
Determine the amplitude, phase shift, period, and vertical shift of the function.
f(x)=4cos(pi/2-1)+4
Amp: 4
Period: 4
Phase Shift: Right 1
Vertical Shift: Up 4
Determine the quadrant in which an angle lies according to the information given.
Angle x has a positive cos value and a coterminal angle of -330 degrees find what quadrant angle x lies in
Angle x is in quadrant IV
Determine the exact value of expressions with compositions of trigonometric and inverse trigonometric functions at any angle.
Determine the value of
Sin(Arccos(1/2))
Arccos(1/2)=pi/3
Sin(pi/3)=sqrt(3)/2
Use the double-angle, half-angle, and product-to-sum formulas to determine exact values of trigonometric expressions and verify identities.
Use the half-angle identity to find the value of cos(75).
sqrt(2+sqrt(3)/2)
Draw one complete cycle of the basic tangent, cotangent, secant, and cosecant non-translated graphs.