HLAA SEM2 practice

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Question 1 of 21

1. Question

(Calculator) In triangle [math]ABC[/math], [math]b=6, c=9[/math], and [math]\angle B=30^\circ[/math]. Find [math]\angle C[/math]. If you have two answers, write the bigger one.

BLANK 1 of 1 degrees
Fill in the blank 1 of 1 degrees

Correct

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Question 2 of 21

2. Question

Consider a triangle [math]ABC[/math] that satisfies [math]a=12, b=10[/math], and [math]c=8[/math]. If the area of [math]ABC[/math] can be written as [math]a\sqrt{b}[/math] where [math]b[/math] is a prime number, what are [math]a [/math] and [math]b[/math]?

[math]a=[/math]BLANK 1 of 2 , [math]b=[/math]BLANK 2 of 2
[math]a=[/math]Fill in the blank 1 of 2 , [math]b=[/math]Fill in the blank 2 of 2

Correct

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Question 3 of 21

3. Question

(Calculator) Determine how many triangles can be formed with the given information. If your answer is “infinite”, just write “inf”

(a) [math]m\angle A=36^\circ, m\angle B=71^\circ, b=3[/math]

(b) [math]m\angle A=51^\circ, c=4, b=11[/math]

(c) [math]m\angle B=40^\circ, a=12, b=9[/math]

(d) [math]a=3, b=12, c=6[/math]

(a) BLANK 1 of 4 triangle(s) (b) BLANK 2 of 4 triangle(s) (c) BLANK 3 of 4 triangle(s) (d) BLANK 4 of 4 triangle(s)
(a) Fill in the blank 1 of 4 triangle(s)

(b) Fill in the blank 2 of 4 triangle(s)

(c) Fill in the blank 3 of 4 triangle(s)

(d) Fill in the blank 4 of 4 triangle(s)

Correct

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Question 4 of 21

4. Question

Which of the following expressions is not equal to 1?

[math]\cos^2x+\sin^2x[/math]

Correct Incorrect Correct answer

[math]\tan^2x-\sec^2x[/math]

Correct Incorrect Correct answer

[math]\csc^2x-\cot^2x[/math]

Correct Incorrect Correct answer

[math]1+\sin40^\circ-\cos50^\circ[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 5 of 21

5. Question

If [math]\sin x=m[/math] where [math]x[/math] is obtuse, which of the following expressions is equivalent to [math]\sin2x[/math]

[math]2m[/math]

Correct Incorrect Correct answer

[math]-m\sqrt{1-m^2}[/math]

Correct Incorrect Correct answer

[math]2m\sqrt{1-m^2}[/math]

Correct Incorrect Correct answer

[math]-2m\sqrt{1-m^2}[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 6 of 21

6. Question

If [math]x=\dfrac{2\pi}{7}[/math], what is [math]\cos2x\cos5x-\sin2x\sin5x[/math]?

BLANK 1 of 1
Fill in the blank 1 of 1

Correct

Incorrect
Question 7 of 21

7. Question

Which of the following forms is equivalent to [math]\dfrac{1-\tan^2x}{1+\tan^2x}[/math]

[math]\sin2x[/math]

Correct Incorrect Correct answer

[math]\cos2x[/math]

Correct Incorrect Correct answer

[math]\csc2x[/math]

Correct Incorrect Correct answer

[math]\sec2x[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 8 of 21

8. Question

What is the value of [math](\sin67.5^\circ-\cos67.5^\circ)^2[/math]?

[math]\dfrac{1}{2}[/math]

Correct Incorrect Correct answer

[math]\dfrac{1}{\sqrt{2}}[/math]

Correct Incorrect Correct answer

[math]1-\dfrac{1}{\sqrt{2}}[/math]

Correct Incorrect Correct answer

[math]1-\dfrac{2}{\sqrt{2}}[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 9 of 21

9. Question

If [math]\tan x=\dfrac{4}{3}[/math] where [math]\pi\leq x\leq2\pi[/math], what is the value of [math]\tan\left(\dfrac{x}{2}\right)[/math]?

BLANK 1 of 1

Fill in the blank 1 of 1

Correct

Incorrect
Question 10 of 21

10. Question

Which of the following forms is equal to [math]\cos40^\circ[/math]?

[math]2\sin20^\circ \cos20^\circ[/math]

Correct Incorrect Correct answer

[math]\cos^220^\circ+\sin^220^\circ[/math]

Correct Incorrect Correct answer

[math]2\sin^220^\circ-1[/math]

Correct Incorrect Correct answer

[math]\cos^220^\circ-\sin^220^\circ[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 11 of 21

11. Question

Find the largest number.

[math]\sin^{-1}1[/math]

Correct Incorrect Correct answer

[math]\cos^{-1}1[/math]

Correct Incorrect Correct answer

[math]\tan^{-1}1[/math]

Correct Incorrect Correct answer

[math]1[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 12 of 21

12. Question

How many solutions does the equation [math]\pi^{\sin x}=e[/math] have?

Zero

Correct Incorrect Correct answer

One

Correct Incorrect Correct answer

Two

Correct Incorrect Correct answer

More than two

Correct Incorrect Correct answer

Correct

Incorrect
Question 13 of 21

13. Question

What is the value of [math]\tan^{-1}(\tan(-2))[/math]?

[math]-2[/math]

Correct Incorrect Correct answer

[math]-2-\pi[/math]

Correct Incorrect Correct answer

[math]-2+\pi[/math]

Correct Incorrect Correct answer

[math]2[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 14 of 21

14. Question

Solve the equation [math]\tan(3x)+1=0[/math]

BLANK 1 of 2[math]\pi+[/math]BLANK 2 of 2[math]k\pi[/math] where [math]k[/math] is an integer.
Fill in the blank 1 of 2 [math]\pi+[/math]Fill in the blank 2 of 2 [math]k\pi[/math] where [math]k[/math] is an integer.

Correct

Incorrect
Question 15 of 21

15. Question

Evaluate [math]-4\tan^{-1}\left(-2\sin\left(\dfrac{1}{2}\cos^{-1}\left(\dfrac{1}{2}\right)\right)\right)[/math]

[math]0[/math]

Correct Incorrect Correct answer

[math]\pi[/math]

Correct Incorrect Correct answer

[math]1[/math]

Correct Incorrect Correct answer

[math]-1[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 16 of 21

16. Question

If [math]\theta=\sin^{-1}\left(-\dfrac{1}{3}\right)[/math], which of the following statements is true?

[math]\theta[/math] is unique

Correct Incorrect Correct answer

[math]\theta[/math] is in the interval [math][\pi, 2\pi][/math]

Correct Incorrect Correct answer

[math]\tan\theta=\dfrac{1}{\sqrt{8}}[/math]

Correct Incorrect Correct answer

[math]\theta[/math] is a solution to the equation [math]3\sin\theta-1=0[/math]

Correct Incorrect Correct answer

Correct

Incorrect
Question 17 of 21

17. Question

What is the solution to the equation [math]\tan2x=1[/math]?

BLANK 1 of 2[math]\pi+[/math]BLANK 2 of 2[math]k\pi[/math] where [math]k[/math] is an integer.
Fill in the blank 1 of 2 [math]\pi+[/math]Fill in the blank 2 of 2 [math]k\pi[/math] where [math]k[/math] is an integer.

Correct

Incorrect
Question 18 of 21

18. Question

Evaluate [math]\cos^{-1}\left(\cos\dfrac{6\pi}{5}\right)[/math]

BLANK 1 of 1[math]\pi[/math]
Fill in the blank 1 of 1 [math]\pi[/math]

Correct

Incorrect
Question 19 of 21

19. Question

How many solution does the equation [math]2\sin\left(4x-\dfrac{\pi}{5}\right), x\in[0, 4\pi][/math] have?

BLANK 1 of 1

Fill in the blank 1 of 1

Correct

Incorrect
Question 20 of 21

20. Question

Evaluate [math]\tan(2\cos^{-1}(-0.4))[/math].

BLANK 1 of 1

Fill in the blank 1 of 1

Correct

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Question 21 of 21

21. Question

Which of the following expressions is equivalent ot [math]\cos(\tan^{-1}x-\tan^{-1}y)[/math]?

[math]\dfrac{x^2+y^2}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

Correct Incorrect Correct answer

[math]\dfrac{1+xy}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

Correct Incorrect Correct answer

[math]\dfrac{x^2-y^2}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

Correct Incorrect Correct answer

[math]\dfrac{1-xy}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

Correct Incorrect Correct answer

Correct

Incorrect

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