Angles
Trig. Functions
Inverse Trig. Functions
Unit Circle
Trig. Identities
100
Convert the angle from radians to degrees and vice versa. Are the answers coterminal to each other?
π/12 radians to degrees
150 degrees to radians
15 degrees & 5π/6 radians.
They are not coterminal.
100
Use reference angles to find the exact value of the expression.
csc
5π/6
=
2
100
Evaluate this inverse function.
sin^−1 (√2/2)
pi / 4 radians
100
Which of the following points is in the unit circle?
a) (-√2 / 2 , -√2 / 2)
b) (√2 / 3 , -√2 / 3)
c) (1 / 2 , 1 / 2)
d) (3 / 2 , 2 / 3)
a
100
Simplify the expression.
sin(x) cos(x) sec(x)
sin(x)
200
Angel baked a pie that has a radius of 3 inches and someone has eaten a 140-degree portion of it. Find the arc length of the eaten portion. Round to two decimal places.
Tony also baked a pie that has an arc length of a sector of 66 cm and the central angle is 30°. Find its radius.
7.33 inches
&
Arc length of a sector = 66 cm
Central angle = 30°
200
Determine the exact trig. function value.
cos (-990 degrees) =
0
200
Evaluate the expression
sin^−1 (cos(π))
-(π/2) radians
200
What quadrant is the point 7π√6 located?
Quadrant III
200
Simplify the expression.
cot(t) + tan(t) / csc(−t)
- sec(t)
300
A central angle θ in a circle of radius 5 m is subtended by an arc of length 6 m. Find the measure of θ in degrees. (Round your answer to one decimal place.)
68.8 degrees
300
Use reference angles to find the exact value of the expression.
sec(240°) =
-2
300
What are the domain and range?
y= arccos(x)
Domain: [-1, 1]
Range: [0, π]
300
Find the exact value of the expression.
cot (15π / 4)
-1
300
Simplify the expression.
cot(x) cos(x) + csc(x) sin^2(x)
csc(x)
400
Use Pythagorean Theorem to determine the hypotenuse's length for a right triangle-shaped piece of carpet that the carpenter needs. Using the sides a = 5 ft and b = 8 ft. Also, determine the area of this carpet.
Length of side c = 9.43
Area = 20 ft
400
The height of a piston, y, in inches, can be modeled by the equation y = 2 cos(x) + 5, where x represents the crank angle. Find the height of the piston when the crank angle is 5°. (Round your answer to two decimal places.)
6.99 in
400
Evaluate the expression.
sin^−1 (sin(5π/3))
-(π/3) radians
400
If cos(t) = − 34, and t is in quadrant III, find the exact values of sin(t), sec(t), csc(t), tan(t), and cot(t).
sin(t) = - (√7 / 4)
sec(t) = - (4 / 3)
csc(t) = - (4 / √7)
tan(t) = √7
cot(t) = 3 / √7
400
Simplify this expression by writing the simplified form in terms of the second expression.
(cos(x) / 1 + sin(x)) + tan(x); cos(x)
1 / cos(x)
500
Use the given information to find the length of a circular arc. Round to two decimal places. The arc of a circle of radius 8.01 miles subtended by the central angle of π/3 radians.
8.39 miles
500
If cos(t) = − 1/5, and t is in quadrant III, find the exact values of sin(t), sec(t), csc(t), tan(t), and cot(t).
sin(t) = (-2√6 / 5)
sec(t) = (-5)
csc(t) = (-5 / 2√6)
tan(t) = (2√6)
cot(t) = (1 / 2√6)
500
A 12-foot ladder leans up against the side of a building so that the foot of the ladder is 6 feet from the base of the building. If specifications call for the ladder's angle of elevation to be between 35 and 45 degrees, does the placement of this ladder satisfy safety specifications?
Angle of elevation = 60 degrees
Ladder placement will not satisfy specifications.
500
The height of a piston, y, in inches, can be modeled by the equation y = 4 cos(x) + 3, where x represents the crank angle. Find the height of the piston when the crank angle is 55°. (Round your answer to two decimal places.)
5.29 in
500
Determine whether the identity is true or false?
csc(θ) + cot(θ) / tan(θ) + sin(θ) = csc^2(θ)
csc(θ) + cot(θ) / tan(θ) + sin(θ) = cot(θ) csc(θ)