Fall 2021 Review for EXAM I-Unit Circle, Right Triangle Trig, Coterminal Angles,

sec(θ)

1/cosθ Hypotenuse/Adjacent

3π/2 or 270°

A 3/4 rotation around the unit circle

1.9

A 4.5 yard long ladder just reaches the top of a wall. The angle between the ladder and the ground is 65 degrees. The distance from the wall to the ladder is ______ yards.

1.60

A 4.9 m ladder leans against a wall and makes an angle of 71 degrees with the ground. How far from the base of the wall is the bottom of the ladder?

One radius length subtended around a circle to form an arc.

A Radian

75.3

A flower garden the shape of a right triangle has a base length of 11.2 feet and a hypotenuse of 17.5 feet. What is the area of this flower bed?

2π or 360°

A full rotation around the unit circle

41

A guy wire to a pole makes an angle of 71.4⁰ with the level ground and is 13.8 feet from the pole at ground level. The guy wire is attached on the pole ______ feet above the ground.

π or 180°

A half rotation around the unit circle

22

A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree, the angle the ladder makes with the wall.

15

A ladder leans against a building. The foot of the ladder is 6 feet from the building. The ladder reaches a height of 14 feet on the building. Find the length of the ladder to the nearest foot.

67

A ladder leans against a building. The foot of the ladder is 6 feet from the building. The ladder reaches a height of 14 feet on the building. Find to the nearest degree, the angle the ladder makes with the ground.

SOHCAHTOA

A mnemonic device to help remember the relationship of the three trig relationships (Sine, Cosine, or Tangent) and the sides they represent. Sine = opp / hyp ; Cos = Adj / hyp ; Tan = opp / adj

5.4

A nursery plants a new tree and attaches a guy wire to help support the tree while its roots take hold. An eight foot wire is attached to the tree and to a stake in the ground. From the stake in the ground the angle of elevation of the connection with the tree is 42º. Find to the nearest tenth of a foot, the height of the connection point on the tree.

π/2 or 90°

A quarter rotation around the unit circle

32

A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?

Trigonometric Ratio

A ratio of the lengths of two sides in a right triangle.

3.3

A road has a rise of 7m for every 120m of horizontal distance. The angle of elevation of this road is ______ degrees.

28

A set of stairs has a vertical rise of 15 cm for every 28 cm of horizontal run. The angle between the stairs and floor is ______ degrees.

30

A six foot tall man casts a 10.6 foot shadow. The angle of elevation of the sun is ______ degrees.

θ

A variable typically used to represent a missing angle measure

All Silver Tea Cups

Acronym for which trig functions are positive in a given quadrant (All, Sine, Tangent, Cosine)

Acronym for which trig functions are positive in a given quadrant (All, Sine, Tangent, Cosine)

All Smart Trig Classes

Angle in standard position

An angle is said to be in standard position if its initial side coincides with the positive x-axis and its vertex coincides with the origin

An angle is said to be in standard position if its initial side coincides with the positive x-axis and its vertex coincides with the origin

Angle in standard position

Angle of Depression

Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.

multiply by π/180

Converting Degrees to Radians

multiply by 180/π

Converting Radians to Degrees

The ratio of the adjacent side of a right triangle divided by the hypotenuse.

Cosine

6.2

Find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58º. Find the length to the nearest tenth of a foot.

10.7

Find x using trig.

15.0406

Find x using trig.

20.0

Find x using trig.

53.6

From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot?

50

How many degrees is angle A if sinA = 0.7612?

Cosine

In a right triangle, the ratio of the side adjacent / the hypotenuse

Sine

In a right triangle, the ratio of the side opposite / the hypotenuse

Tangent

In a right triangle, the ratio of the side opposite / the side adjacent

starting position of the rotated ray in the formation of an angle

Initial side of an angle

3π/3

Name an angle coterminal to -3π/3

285⁰

Name an angle coterminal to -435⁰

278⁰

Name an angle coterminal to -442⁰

-90⁰

Name an angle coterminal to 270⁰

640⁰

Name an angle coterminal to 280⁰

-4π/3

Name an angle coterminal to 2π/3

-330⁰

Name an angle coterminal to 30⁰

-2π/3

Name an angle coterminal to 4π/3

11π/3

Name an angle coterminal to 5π/3

7π/3

Name an angle coterminal to π/3

sin²θ + cos²θ = 1

Pythagorean Identity

3-4-5 5-12-13 8-15-17

Pythagorean Triplet

(+,+)

Quadrant I

(-,+)

Quadrant II

(-,-)

Quadrant III

(+,-)

Quadrant IV

The ratio of the side opposite of a right triangle divided by the hypotenuse for a right triangle.

Sine

refers to the 45-45-90 and 30-60-90 right triangles

Special Right Triangles

The ratio of the side opposite of a right triangle divided by the adjacent side for a right triangle.

Tangent

the ray where measurement of an angle stops

Terminal side of an angle

Angle of Elevation

The angle above horizontal that an observer must look to see an object that is higher than the observer; it is congruent to the angle of depression

Adjacent Side

The leg next to the given angle in a right triangle. The "adjacent side" and the hypotenuse will always create the angle of reference.

Radian

The measure of a central angle of a circle whose intercepted arc measures one radius in length

Opposite Side

The side of a polygon not used to create the angle of reference. The angle of reference is composed of the hypotenuse and the side adjacent. The opposite side is the third side not touching the angle of reference.

51.3

Triangle ABC is right angled at B. Angle A is 48.81⁰ and side a is 16 cm. The perimeter of this triangle is _____ cm.

15/cos 54⁰

Triangle DEF is right angled at F. Angle E is 36 degrees and DF = 15cm. The length of DE is determined by ______.

33

Triangle PQR has the following dimensions: Angle Q is 90 degrees, angle R is 28 degrees and PQ = 15.6 mm. The hypotenuse of Triangle PQR is ______ mm.

A ratio of the lengths of two sides in a right triangle.

Trigonometric Ratio

a circle with a radius of 1, centered at the origin

Unit Circle

5/12

What is the value of cosB in right triangle ABC, if AB = 52 units, AC = 48 units, and BC = 20 units?

Unit Circle

a circle with a radius of 1, centered at the origin

1

cos(2π)

√3/2

cos(315°)

1/2

cos(π/3)

1/tanθ cos(θ)/sin(θ) Adjacent/Opposite

cot(θ)

1/sinθ Hypotenuse/Opposite

csc(θ)

Converting Radians to Degrees

multiply by 180/π

Converting Degrees to Radians

multiply by π/180

1/cosθ Hypotenuse/Adjacent

sec(θ)

-√3/2

sin(240°)

-√2/2

sin(5π/4)

0

sin(π)

Pythagorean Identity

sin²θ + cos²θ = 1

Initial side of an angle

starting position of the rotated ray in the formation of an angle

Trigonometry

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Terminal side of an angle

the ray where measurement of an angle stops

cos(θ)

x-coordinate for the unit circle

sin(θ)

y-coordinate for the unit circle

Theta

Θ - variable used in trigonometry to indicate an angle measure