2Q_SUMMATIVE TEST_PRECALCULUS

A circle has a radius of 8 meters. A central angle measures 315°. What is the length of the corresponding arc?

• 7π meters

• 10π meters

• 14π meters

• 16π meters

A circle has a diameter of 8 meters. The area of a sector of this circle is 16 m². What is the length of the arc that forms the boundary of this sector?

• 4 meters

• 6 meters

• 8 meters

• 10 meters

Jasmine checks whether the equation (cos x + tan x cos x = 1) / (sin x + cot x sin x) is an identity or a conditional equation. After simplifying, both sides are equal. Which statement correctly describes the equation?

• The equation is contradiction because it has no real solution.

• The equation is identity because it got a true statement, which is 1 = 1.

• The equation is conditional because it got a true statement, which is 1 = 1.

• The equation is contradiction because it got a true statement, which is 1 = 1.

During a mountain survey, a drone measures angles of elevation and depression using trigonometric sensors. The software displays values that must stay within the range of the inverse secant function y = arcsec x. To ensure readings, which of the following values cannot be used as input/domain for y = arcsec x?

• x = -3

• x = -1

• x = 0.5

• x = 2

What is the reference angle of 240°?

• 60°

• –60°

• 240°

• –240°

Maria is learning to use reference angles to find exact values of circular functions and she is given an angle 240°. What is sin 240°?

• 1/2

• √3/2

• –1/2

• –√3/2

Janela, a grade 11 STEM student is studying the graph of the function y = sec 3(x – π/4) + 1. She knows that the secant function is undefined where its corresponding cosine function equals zero. Which of the following correctly represents the values of x that must be excluded from the domain?

• x = 4π/12 + nπ/3, n ∈ Z

• x = 4π/12 – nπ/3, n ∈ Z

• x = 5π/12 + nπ/3, n ∈ Z

• x = 5π/12 – nπ/3, n ∈ Z

Ivan is a student under STEM strand and he is simplifying the expression (cos x + sin²x + cos²x) / cos²x. After applying trigonometric identities, what is the correct simplified form in terms of cos x?

(a)  

If Ivan would simplify the expression (cos x + sin²x + cos²x) / cos²x in terms of sec x, what will be the outcome?

• 1/(sec x + 1)

• 1/(sec x - 1)

• sec x/(sec x - 1)

• sec x/(sec x + 1)

A navigation software in a submarine uses trigonometric models to calculate the angle of sonar waves underwater. One model uses the equation y = (3/4)sin(-2x) to describe the sonar signal path. To reverse-engineer the signal angle from the measured output y, the system must find the inverse function of the equation. Which of the following expressions correctly represents the inverse function of y = (3/4)sin(-2x)?

• y = -1/2 arcsin(4/3 x)

• y = -2arcsin(4/3 x)

• y = 2arcsin(4/3 x)

• y = 1/2 arcsin(4/3 x)