Special Right Triangles
What do the legs of a 45-45-90 triangle equal?
x
What is the reference angle for a 160-degree angle?
20 degrees
In which quadrants is sin positive according to ASTC?
Quadrants I and II
Solve the following for θ: 9 tan θ = -12. Round your answers to the nearest tenth.
θ = 126.9 degrees, 306.9 degrees
Write out the formula for sec θ in terms of opposite, adjacent, and hypotenuse.
sec θ = Hypotenuse / Adjacent
What does the long leg of a 30-60-90 triangle equal?
x√3
What is the reference angle for a 237-degree angle?
57 degrees
In which quadrants is tangent negative according to ASTC?
Quadrants II and IV
Solve the following for θ: 3 cos θ - 1 = 0. Round your answers to the nearest tenth.
θ = 70.5 degrees, 289.5 degrees
Write out the formula for cot θ in terms of opposite, adjacent, and hypotenuse.
Cot θ = Adjacent /Opposite
If one leg of a 45-45-90 triangle equals 4, what are the values of the other leg and the hypotenuse?
Leg = 4
Hypotenuse = 4√2
Use a reference triangle to find the value of the following trig function: cos 45 degrees.
√2 / 2
For an angle measuring 197 degrees, which trig functions would be negative?
Sine and cosine
Solve the following for θ: 9 sin θ + 8 = 0. Round your answers to the nearest tenth.
θ = 242.7 degrees, 297.3 degrees
Write out the formula for csc θ in terms of opposite, adjacent, and hypotenuse.
csc θ = Hypotenuse / Opposite
If the short leg of a 30-60-90 triangle equals 3, what are the values of the long leg and hypotenuse?
Long Leg = 3√3
Hypotenuse = 6
Use a reference triangle to find the value of the following trig function: tan 120 degrees.
-√3
Describe the meaning behind the acronym ASTC.
A = All trig functions are positive in quadrant I
S = Sine is positive in quadrant II
T = Tangent is positive in quadrant III
C = Cosine is positive in quadrant IV
Solve the following for θ: tan2 θ = 3. Round your answers to the nearest tenth.
θ = 60 degrees, 120 degrees, 240 degrees, 300 degrees
Match the following reciprocal trig function to the basic trig functions.
(a) Cot θ
(b) Csc θ
(c) Sec θ
(a) Tan θ
(b) Sin θ
(c) Cos θ
If the long leg of a 30-60-90 triangle equals 9, what are the values of the short leg and hypotenuse?
Short Leg = 3√3
Hypotenuse = 6√3
Use a reference triangle to find the sine, cosine, and tangent of θ if θ = 315 degrees.
Sin θ = -√2 / 2
Cos θ = √2 / 2
Tan θ = -1
Find the values for the other two trig functions using the following information: cos θ = 2/3 and sin θ > 0.
Sin θ = √5 / 3
Tan θ = √5 / 2
Solve the following for θ: 9 sin2 θ - 3 = 0. Round your answers to the nearest tenth.
θ = 35.3 degrees, 144.7 degrees, 215.3 degrees, 324.7 degrees
Find the six trig function values for the given reference angle.
Sin θ = 8/17
Cos θ = 15/17
Tan θ = 8/15
Csc θ = 17/8
Sec θ = 17/15
Cot θ = 15/8