Angle Measure
The 1 and Only
Unit Circle
Caught in a
Love Triangle
Model
Talk It Like
I Walk It
100

Convert

`theta=156^o`

 to exact radian measure (simplify your answer).

`theta=(13pi)/15`

100

Evaluate the exact value of

`sin ((7pi)/4)=`

`y=-sqrt2/2`

100

Find the exact value of "x".

`4sqrt3`

100

If AC is 47 meters, find the approximate height of the tree (round to the tenths).


32.9 meters

100

Degrees and radians are the units used when measuring what quantity?

Rotation

200

Find one positive angle (in exact radian measure) that is coterminal to 

`-(18pi)/4`

`theta=(3pi)/2`

200

Evaluate the exact value of

`cos (-(7pi)/6)=`

`x=-sqrt3/2`

200

Find the exact value of x.

`x=8`

200

Find the approximate height of a tree meters (round to the nearest tenth).

6.7 meters

200

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

300

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`

300

Estimate to the nearest tenth.

`sin((29pi)/24)approx`

`yapprox-0.6`

300

Find the approximate value of x in degrees.  

Round to the tenths place (image not to scale).

`xapprox66.8^o`

300

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`

300

Secant, cosecant and cotangent have a relationship with cosine, sine and tangent respectively.  What is that relationship?

Reciprocals

400

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`

400

Evaluate the exact value of

`cot ((14pi)/3)=`

`-sqrt3/3`

400

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`

400

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

400

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

500

Given that the angle

`angleCOD`

 is 0.4 radians, find the length of the radius OB.

`OB=4.5 cm`

500

Evaluate the exact value of the expression over the interval 

`0<=theta<=2pi`

`
`

`tan^-1(csc(-(3pi)/2))=`

`theta=(pi)/4, (5pi)/4`

500

Write an algebraic expression for

`sec(theta)`

 in terms of x.

`sec(tan^-1((3x)/5))`

`sec(theta)=sqrt(9x^2+25)/5`

500

Solve for the approximate height of the pyramid (distance from base to point E).  Round to the hundredths place.

`happrox9.77 cm`

500

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.