Convert
`theta=156^o`
to exact radian measure (simplify your answer).
`theta=(13pi)/15`
Evaluate the exact value of
`sin ((7pi)/4)=`
`y=-sqrt2/2`
Find the exact value of "x".
`4sqrt3`
If AC is 47 meters, find the approximate height of the tree (round to the tenths).
32.9 meters
Degrees and radians are the units used when measuring what quantity?
Rotation
Find one positive angle (in exact radian measure) that is coterminal to
`-(18pi)/4`
`theta=(3pi)/2`
Evaluate the exact value of
`cos (-(7pi)/6)=`
`x=-sqrt3/2`
Find the exact value of x.
`x=8`
Find the approximate height of a tree meters (round to the nearest tenth).
6.7 meters
List 3 features that define a Unit Circle.
1. Radius of one unit
2. Centered at the origin (0,0)
3. Comprised of Special Right Triangles
The terminal side of an angle is in quadrant 3. If the cosine of that angle is -13/15, find the approximate value of the reference angle
`theta'`
in radians, round to the nearest hundredth.
`theta'approx0.52`
Estimate to the nearest tenth.
`sin((29pi)/24)approx`
`yapprox-0.6`
Find the approximate value of x in degrees.
Round to the tenths place (image not to scale).
`xapprox66.8^o`
Two cables, s and r, are attached to a flag pole. The combined length of the cables is 50 feet. Find x to the nearest tenth of a degree.
`x^oapprox32.2^o`
Secant, cosecant and cotangent have a relationship with cosine, sine and tangent respectively. What is that relationship?
Reciprocals
If the cosine & tangent ratios of a right triangle created by an angle are negative and the reference angle is
`theta=(3pi)/11`
radians, find the original positive angle in exact radians.
`theta=(8pi)/11`
Evaluate the exact value of
`cot ((14pi)/3)=`
`-sqrt3/3`
Each triangle below is a 30-60-90 triangle. The hypotenuse of the triangle to the right is twice as long as the long leg of the triangle to the left. If the short leg of the smallest triangle is given. Find the exact value of "a".
`a=9`
A cylinder with a radius of 12 cm rotates at an angular speed of 5 radians per second. Find the linear speed of a point on the edge of the cylinder in meters per second.
0.6 m/s
What is the amount of rotation that has occurred between two radii of a circle when the arc length along the edge of the circle is equal to the radius of the circle?
1 radian
Given that the angle
`angleCOD`
is 0.4 radians, find the length of the radius OB.
`OB=4.5 cm`
Evaluate the exact value of the expression over the interval
`0<=theta<=2pi`
`
`
`tan^-1(csc(-(3pi)/2))=`
`theta=(pi)/4, (5pi)/4`
Write an algebraic expression for
`sec(theta)`
in terms of x.
`sec(tan^-1((3x)/5))`
`sec(theta)=sqrt(9x^2+25)/5`
Solve for the approximate height of the pyramid (distance from base to point E). Round to the hundredths place.
`happrox9.77 cm`
What is the relationship between
`(2pi)/5`
and the following angles:
`(3pi)/5,-(7pi)/5,(13pi)/5,-(17pi)/5`
`(2pi)/5`
is the reference angle for all those angles.