Basic Trig Functions
What are the three basic trig functions?
Sin, cos, and tan
Find sin(0).
0
When should we use the law of sines?
When there’s at least one pair of an opposite angle and side
solve sin(x) = 1/2 on the domain (0, 2π).
x = π/6, 5π/6
Name any four major properties of a trig graph.
Amplitude, midline, period, phase shift, vertical shift
What is the sin of a right triangle with
opposite - 4
adjacent - 3
hypotenuse - 5
4/5
Find cos(180)
-1
All the angles in a triangle add up to how many degrees?
180
Expand sin(2x).
2sin(x)cos(x)
What is the midline of a graph with a vertical shift of 4?
y = 4
Find the sec of a right triangle with
opposite - 5
adjacent - 12
hypotenuse - 13
Find tan(90)
Undefined
Two of the angles in a triangle are 95 and 63. What is the last angle?
22 degrees
Expand sin(a + b).
sin(a)cos(b) + sin(b)cos(a)
What is the period of tan(x)?
π
Find the cos of a right triangle with
opposite - 7
adjacent - 24
24/25
Find cot(270)
0
Triangle ABC has angle A = 106°, angle B = 31° and side a = 10 cm. Find the other two sides.
Solve sin2(x) - 5sin(x) + 6 = 0
No solutions
What is the phase shift of the graph 2sin(3x + 2)?
2/3
Find cos(x) if sin(x) = 9/41
40/41
Find sin(60)
sqrt3 / 2
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
Generalize the steps to proving a trig identity.
Convert everything to sin and cos, using reciprocal identities and quotient identities.
Simplify the sides as much as you can, using some identities that you already know.
Factor numerator and denominator(if there are any).
Cancel out any terms.
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