12th
grade

Mathematics

69%

accuracy

504

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English Casbarro

3 years

Mathematics

12th

grade

Trig Identities

English Casbarro

504
plays

20 questions

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1. Multiple Choice
30 seconds
1 pt
$\tan\theta\ =$
$\frac{\sin\theta}{\cos\theta}$
$\frac{\cos\theta}{\sin\theta}$
$\frac{1}{\cos\theta}$
$\cot\theta$
2. Multiple Choice
30 seconds
1 pt
$\sin^2\theta\ +\ \cos^2\theta\ =\ 1$

Solve for $\cos^2\theta$ .
$\cot^2\theta+1$
$\sec^2\theta-1$
$\tan\theta+1$
$1-\sin^2\theta$
3. Multiple Choice
30 seconds
1 pt
$\tan\theta\cos\theta$ can be written in a single trigonometric identity as:
$\cos\theta$
$\sin\theta$
$\sec\theta$
$\cot\theta$
4. Multiple Choice
30 seconds
1 pt
$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:
$\cos^2\theta$
$\sin^2\theta$
$\sec^2\theta$
$\tan^2\theta$
5. Multiple Choice
30 seconds
1 pt
$\cos\theta\ \csc\theta$ can be written in a single trigonometric identity as:
$\cos\theta$
$\sin\theta$
$\sec\theta$
$\cot\theta$
6. Multiple Choice
3 minutes
1 pt
Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$
csc²θ
sec²θ
cscθ
1
7. Multiple Choice
3 minutes
1 pt
Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$
$\sec\theta$

$\cos^2\theta$
$\sin^2\theta$
$\frac{\sin^2\theta}{\cos^2\theta}$
8. Multiple Choice
3 minutes
1 pt
Simplify

$\tan x\csc x\cos x$
$\frac{1}{\cos x}$
1
$\cot x$
-1
9. Multiple Choice
15 minutes
1 pt
Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$
$2\sec\theta$
$\cot^2\theta$
$\tan^2\theta$
$\sec^2\theta+1$
10. Multiple Choice
15 minutes
1 pt
Simplify

$\csc\ x\left(\cos x+\sin x\right)$
csc x
tan x + 1
cot x
cot x + 1
11. Multiple Choice
15 minutes
1 pt
Simplify $\tan x\left(\cot x\ +\ \csc x\right)$
$1\ +\ \sec x$
$1\ +\ \csc x$
$\sec x-1$
$\tan^2x$
12. Multiple Choice
30 seconds
1 pt
$\frac{1-\cos^2\theta}{\tan^2\theta}$ can be simplified as
$\cot^2\theta$
$\tan^2\theta$
$\sin^2\theta$
$\cos^2\theta$
13. Multiple Choice
30 seconds
1 pt
What happens when you multiply two reciprocal functions?
You get a pythagorean identity
It equals 1
You get a quotient identity
It equals 0
14. Multiple Choice
2 minutes
1 pt
Which of the following would be a step to prove the following identity? $\csc x-\sec x=\frac{\cos x-\sin x}{\sin x\cos x}$
$\frac{1}{\sin x}-\frac{1}{\cos x}$
$\frac{\cos x-\sin x}{\sin x}$
$\frac{\cos x-\sin x}{\cos x}$
$\frac{1}{\sin x\cos x}$
15. Multiple Choice
30 seconds
1 pt

One step in proving the identity below would be:

$\frac{\sec^2\theta-1}{\sec^2\theta}$
$\frac{\sec^2\theta}{\sec^2\theta}-\frac{1}{\sec^2\theta}$
$\frac{\tan^2\theta}{\sec^2\theta}$
Both A and B
Neither A nor B
16. Multiple Choice
30 seconds
1 pt
$\frac{\tan\theta+\cot\theta}{\tan\theta}$ can be simplified as:
$\csc^2\theta$
$\cot^2\theta$
$\sin^2\theta$
$\cos^2\theta$
17. Multiple Choice
30 seconds
1 pt
$\sin\theta\cot\theta\ \sec\theta$
$0$
$1$
$\sin\theta$
$\cos\theta$
18. Multiple Choice
15 minutes
1 pt
Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$
2secθ
cot²θ
tan²θ
sec²θ + 1
19. Multiple Choice
15 minutes
1 pt
Simplify

$\csc\ x\left(\cos x+\sin x\right)$
csc x
tan x + 1
cot x
cot x + 1
20. Multiple Choice
10 seconds
1 pt
Rewrite $\tan x$ in terms of $\sin x$ and $\cos x$
$\tan x=\frac{\cos x}{\sin x}$
$\tan x=\frac{1}{\cot x}$
$\tan x=\frac{\sin x}{\cos x}$
$\tan x=\frac{opposite}{adjacent}$
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