Basic Trig Functions

Unit circle
Laws of Sine and Cosine
Trig equations and angle formulas
Trig graphs
100

What are the three basic trig functions?

Sin, cos, and tan

100

Find sin(0).

0

100

When should we use the law of sines?

When there’s at least one pair of an opposite angle and side

100

solve sin(x) = 1/2 on the domain (0, 2π).

x = π/6, 5π/6

100

Name any four major properties of a trig graph.

Amplitude, midline, period, phase shift, vertical shift

200

What is the sin of a right triangle with

opposite - 4

adjacent - 3

hypotenuse - 5

4/5

200

Find cos(180)

-1

200

All the angles in a triangle add up to how many degrees?

180

200

Expand sin(2x).

2sin(x)cos(x)

200

What is the midline of a graph with a vertical shift of 4?

y = 4

300

Find the sec of a right triangle with

opposite - 5

adjacent - 12

hypotenuse - 13

13/12
300

Find tan(90)

Undefined

300

Two of the angles in a triangle are 95 and 63. What is the last angle?

22 degrees

300

Expand sin(a + b).

sin(a)cos(b) + sin(b)cos(a)

300

What is the period of tan(x)?

π

400

Find the cos of a right triangle with

opposite - 7

adjacent - 24

24/25

400

Find cot(270)

0

400

Triangle ABC has angle A = 106°, angle B = 31° and side a = 10 cm. Find the other two sides.

400

Solve sin2(x) - 5sin(x) + 6 = 0

No solutions

400

What is the phase shift of the graph 2sin(3x + 2)?

2/3

500

Find cos(x) if sin(x) = 9/41

40/41

500

Find sin(60)

sqrt3 / 2

500

If sides of a triangle are 5.5 and 4.7 respectively. Angle opposite to the side 5.5 is 63 degrees. Find the angle opposite to the side 4.7 to the nearest tenth.

49.6

500

Generalize the steps to proving a trig identity.

  1. Convert everything to sin and cos, using reciprocal identities and quotient identities.

  2. Simplify the sides as much as you can, using some identities that you already know.

  3. Factor numerator and denominator(if there are any).

  4. Cancel out any terms.

500

What is the equation of a cos graph with amplitude of 2, period of π, phase shift of 0, and vertical shift of -1?

2cos(2x) - 1

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