#1
What is the value of sin(90°)?
1
ExplanationSine of 90° is the maximum value in the unit circle.
#2
What is the value of cos(0°)?
1
ExplanationCosine of 0° is the maximum value in the unit circle.
#3
What is the value of tan(45°)?
1
ExplanationTan of 45° is equal to the ratio of the sides in a 45-45-90 triangle.
#4
Which of the following is an identity for cosine?
sin^2(x) = 1 - cos^2(x)
ExplanationThis is the Pythagorean identity for cosine.
#5
What is the period of the function y = 2sin(3x)?
2π
ExplanationThe period of a sine function is 2π divided by the coefficient of x.
#6
Which of the following is an identity for tangent?
cot(x) = cos(x)/sin(x)
ExplanationThis is the reciprocal relationship between tangent and cotangent.
#7
What is the amplitude of the function y = 4cos(2x)?
4
ExplanationThe amplitude of a cosine function is the coefficient of cosine.
#8
Which of the following is NOT a Pythagorean identity?
tan(x) = sin(x)/cos(x)
ExplanationThis is the definition of tangent, not a Pythagorean identity.
#9
If sin(θ) = 3/5 and θ is in quadrant II, what is cos(θ)?
-4/5
ExplanationIn quadrant II, cosine is negative and determined by the Pythagorean theorem.
#10
If tan(θ) = -√3 and θ is in quadrant III, what is sin(θ)?
-1/2
ExplanationIn quadrant III, sine is negative and determined by the Pythagorean theorem.
#11
What is the period of the function y = tan(x)?
2π
ExplanationThe period of tangent is π.